Question

tan theta into sin theta​

Answer 1

Answer:

tan x ×sin x =sin^2x/cosx

1/cos x - cos^2 x /cos x

sec x - cos x

Answer 2

So this is a very interesting question and it can be solved through two methods but answers will be different.

Method 1 -

$Tan\alpha = sin\alpha$ ÷ $cos\alpha$

Squaring both sides

$tan^2\alpha = sin^2\alpha$ ÷ (1 - $sin^2\alpha$)    [applying identity]

$tan\alpha = \sqrt{sin^2\alpha/1 - sin^2\alpha }$

Method 2 -

(using half angle identity)

$sin2\alpha = 2tan\alpha / 1 + tan^2\alpha$

Now put $tan\alpha$ as y and solve the quadratic equation, you will get,

$tan\alpha = 2 + \sqrt{4 - 4sin^22\alpha } / 2sin2\alpha$

There you have your answers, i have put my valuable time into this answer so please mark it the Brainliest please :)