Question

sin2A= 2cotA/sec2A. A=30




5th pls ​

Answer 1

Question :-

$5. \sf \red{ verify \: } \green{\sin2 \theta = \frac{2 \cot \theta}{ \sec2 \theta} } \: \: for \: \red{ \theta = 30 \degree }$

Explanation :-

Just taking both LHS and RHS

$\implies \: \green{\sin2 \theta = \frac{ \red{2 \cot \theta}}{ \purple{\sec2 \theta}} } \: \\ \\ \sf \: put \: \: \theta = 30 \:degree \\ \\ \implies \: \sin( 2 \times 30) \degree = \frac{2 \cot 30 \degree}{ \green{\sec(2 \times 30) }\degree} \\ \\ \implies \: \sin60 \degree = \red{ \frac{2 \cot 30 \degree}{ \sec60 \degree} } \\ \\ \because \: \sin 60 = \frac{ \sqrt{3} }{2} \: \: \\ \: \: \: \: \: \cot30 = \sqrt{3} \\ \: \: \: \: \: \sec 60 = 2 \\ \\ \red{ \therefore \: } \\ \: \\ \to \: \frac{ \sqrt{3} }{2} = \frac{ \sqrt{3} }{2}$

Verified .