Answer

Verified

339k+ 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\]

\[\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

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

And such too is the grandeur of the dooms We have imagined class 12 english CBSE

Where is the endless fountain of immortal drink pouring class 10 english CBSE

What I want should not be confused with total inactivity class 12 english CBSE

Why was the Moral Rearmament Army welcomed at the class 12 english CBSE

Difference Between Plant Cell and Animal Cell