Question

Sin theta = 12/13 find sin 2 theta - cos 2 theta / 2 sin theta. Cos theta x 1/ tan 2 theta

Answer 1

Here is the answer for your question above

Answer 2

given

sinθ = 12/13

we know that

cosθ= √1 - sin²θ

cosθ=√1 - (144/169)

cosθ=√25/169

cosθ=5/13

Also

tanθ=sinθ/cosθ

tanθ=(12/13)/(5/13)

tanθ=12/5

we have to find

(sin²θ-cos²θ/2sinθcosθ) × (1/tan²θ)

$= \frac{ (\frac{12}{13} ) ^{2} - (\frac{5}{13}) ^{2} }{2 \times \frac{12}{13} \times \frac{5}{13} } \times \frac{1}{( { \frac{12}{5} })^{2} } \\ \\ = \frac{144 - 25}{120} \times \frac{25}{144} \\ \\ = \frac{119}{120} \times \frac{25}{144} \\ \\ = \frac{595}{3456}$