How do you solve $tan 1/2x + 2 sin 2x = csc x$ ?

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Answer 1 · 2015-05-31T16:07:18

The question is not clear enough.

I can only suggest a way to solve this equation.

Call $tan (x/2) = t$ . Replace sin x and cos x in terms of t.

$2sin 2x = 4sin x.cos x = 4((2t)/(1 + t^2))((1 - t^2)/(1 + t^2))$

$csc x = 1/sin x = (2t)/(1 + t^2).$

Next solve for $t = tan (x/2)$

How do you solve tan 1/2x + 2 sin 2x = csc xtan 1/2x + 2 sin 2x = csc x?