NCERT Class 11-Math's: Chapter –3 Trigonometric Functions Part 14

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Question 23:

If has α and β as its roots, then prove that

Answer:

Given,

a d α and β are the roots of the equation.

Using the formula of multiple angles, we know that –

and

Clearly it is a quadratic equation in and as and are its solutions.

and are the roots of this quadratic equation.

We know that sum of roots of a quadratic equation:

Hence,

Question 24:

If then show that

Answer:

Given,

To prove:

Thus,

Question 25:

If lies in the first quadrant and then find the value of

Answer:

Question 26:

Find the value of the expression

Answer:

Question 27:

Find the general solution of the equation

Answer:

Question 28:

Find the general solution of the equation

Answer:

Question 29:

Find the general solution of the equation

Answer: