
Solve the following :
Answer
417.6k+ views
Hint: Now to solve this question we need to simplify all the trigonometric functions using their formulas. We convert them into sine and cos functions using the formulas that and . Now students will also need to use the formula that to further simplify and solve this equation and find the necessary answer we need in this question.
Complete step-by-step answer:
Now here in this question we need to find the value of the expression . Now to find its value we can name the expression to be
Now to solve this further we will start by making these equations in the form of sine and cos functions to make it simpler to solve. To convert the equation we use the formula of secant and cot that and . By substituting these values in the above given expression we get
Now we take the first and third term of this equation and taking its LCM we get
Now in first term to simplify it further we multiply and divide both the numerator and denominator by 2 giving us
Now we know that we can write and we can also write
Now we can see that the numerator of first term is in the form of therefore we can see that a is and b is . So we can write this equation is
We can also write in the form of half angle of sine which gives us and we also know that negative angle of sine is always equal to negative of sine that is ; Therefore putting these values we get;
Now cancelling the common terms from both numerator and denominator
Therefore we get
So we can say that ;
Note: To solve questions like this students should always try to remember the half angle and double angle formulas of functions. Converting them into sine and cos functions gives us a way to easily simplify these expressions. Students must also know the product and addition formulas of trigonometric functions. Another necessity required is to know the trigonometric values of all basic angles.
Complete step-by-step answer:
Now here in this question we need to find the value of the expression
Now to solve this further we will start by making these equations in the form of sine and cos functions to make it simpler to solve. To convert the equation we use the formula of secant and cot that
Now we take the first and third term of this equation and taking its LCM we get
Now in first term to simplify it further we multiply and divide both the numerator and denominator by 2 giving us
Now we know that we can write
Now we can see that the numerator of first term is in the form of
We can also write
Now cancelling the common terms from both numerator and denominator
Therefore we get
So we can say that ;
Note: To solve questions like this students should always try to remember the half angle and double angle formulas of functions. Converting them into sine and cos functions gives us a way to easily simplify these expressions. Students must also know the product and addition formulas of trigonometric functions. Another necessity required is to know the trigonometric values of all basic angles.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

What is the technique used to separate the components class 11 chemistry CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
