Answer
Verified
411.3k+ views
Hint:Consider the trigonometric functions to expand the equation with respect to its angles given. So that it will be cancelled easily and we will get the desired value.
Complete step by step answer:
To find the value of
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}}\]
We must know the Trigonometric function chart which helps us to find the values of the function very easily.
Let us write the given terms
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}}\]
As we cannot find the direct value of \[\sin {53^ \circ }\], hence let us split the value into \[\sin
\left( {90 - 37} \right)\], we know that the value of tan45 then the equation becomes
\[ = \dfrac{{\sin \left( {90 - 37} \right)}}{{\cos 37}} + 2\left( 1 \right) - \dfrac{{\cos ec\left( {90 - 30}
\right)}}{{\sec 30}}\]
\[ = \dfrac{{\cos 37}}{{\cos 37}} + 2 - \dfrac{{\sec 30}}{{\sec 30}}\]
\[ = 1 + 2 - 1\]
\[ = 2\]
Therefore, the value of
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}} = 2\]
Additional information:
In trigonometry sin, cos and tan values are the primary functions we consider while solving
trigonometric problems. These trigonometry values are used to measure the angles and sides of a right-angle triangle. Apart from sine, cosine and tangent values, other values are cotangent, secant and cosecant.
When we find sin, cos and tan values for a triangle, we usually consider these angles: 0°, 30°, 45°, 60° and 90°. The trigonometric values are about the knowledge of standard angles for a given triangle as per the trigonometric ratios. Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant.
These angles can also be represented in the form of radians such as 0, π/6, π/4, π/3, and π/2. These angles are most commonly and frequently used in trigonometry.
Note: The key point to find the values of any trigonometric function is to note the chart of all functions as shown and calculates all the terms asked. And here are some of the formulas to be noted.
Tan θ = sin θ/cos θ
Cot θ = cos θ/sin θ
Sin θ = tan θ/sec θ
Cos θ = sin θ/tan θ
Sec θ = tan θ/sin θ
Cosec θ = sec θ/tan θ
Complete step by step answer:
To find the value of
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}}\]
We must know the Trigonometric function chart which helps us to find the values of the function very easily.
Let us write the given terms
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}}\]
As we cannot find the direct value of \[\sin {53^ \circ }\], hence let us split the value into \[\sin
\left( {90 - 37} \right)\], we know that the value of tan45 then the equation becomes
\[ = \dfrac{{\sin \left( {90 - 37} \right)}}{{\cos 37}} + 2\left( 1 \right) - \dfrac{{\cos ec\left( {90 - 30}
\right)}}{{\sec 30}}\]
\[ = \dfrac{{\cos 37}}{{\cos 37}} + 2 - \dfrac{{\sec 30}}{{\sec 30}}\]
\[ = 1 + 2 - 1\]
\[ = 2\]
Therefore, the value of
\[\dfrac{{\sin {{53}^ \circ }}}{{\cos {{37}^ \circ }}} + 2\tan {45^ \circ } - \dfrac{{\cos ec{{60}^ \circ
}}}{{\sec {{30}^ \circ }}} = 2\]
Additional information:
In trigonometry sin, cos and tan values are the primary functions we consider while solving
trigonometric problems. These trigonometry values are used to measure the angles and sides of a right-angle triangle. Apart from sine, cosine and tangent values, other values are cotangent, secant and cosecant.
When we find sin, cos and tan values for a triangle, we usually consider these angles: 0°, 30°, 45°, 60° and 90°. The trigonometric values are about the knowledge of standard angles for a given triangle as per the trigonometric ratios. Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant.
These angles can also be represented in the form of radians such as 0, π/6, π/4, π/3, and π/2. These angles are most commonly and frequently used in trigonometry.
Note: The key point to find the values of any trigonometric function is to note the chart of all functions as shown and calculates all the terms asked. And here are some of the formulas to be noted.
Tan θ = sin θ/cos θ
Cot θ = cos θ/sin θ
Sin θ = tan θ/sec θ
Cos θ = sin θ/tan θ
Sec θ = tan θ/sin θ
Cosec θ = sec θ/tan θ
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE