Question

cosec15+sec15 using formula​

Answer 1

CORRECT QUESTION:

• Cosec15° + sec15°

SOLUTION:

$= \csc15 \degree \: + \: \sec15 \degree \: \\ \\ = \frac{1}{ \sin15 \degree \: } \: + \: \frac{1}{ \cos15 \degree \: } \\ \\ \therefore \: \frac{ \cos15 \degree \: + \: \sin15 \degree }{ \sin15 \degree \: \times \: \cos15 \degree}$

On multiplying 1/✔2 on numerator and denominator we get ,

$= \frac{ \frac{1}{ \sqrt{2} } \cos15 \degree \: + \: \frac{1}{ \sqrt{2} } \sin15 \degree}{ \frac{1}{ \sqrt{2} } \sin15 \degree \: \times \: \frac{1}{ \sqrt{2} } \cos15 \degree}$

On numerator we will apply ,

sin A cos B+ cos A sin B = sin ( A+B ).

On denominator we will apply ,

2sin A × cosA = Sin2 A.

$= \: \frac{ \sin(45 + 15) }{ \frac{1}{2 \sqrt{2} } \sin30 \degree \: } \\ \\ = \frac{2 \sqrt{2} \sin(60) }{ \sin30 \degree} \\ \\ = \frac{2 \sqrt{2} \: \times \: \frac{ \sqrt{3} }{2} }{ \frac{1}{2} } \\ \\ = 2 \sqrt{6} \\ \\ \therefore \: \csc15 \degree \: + \sec15 \degree \: = 2 \sqrt{6}$