Q9 of 113 Page 575

Prove that
sin 2x(tan x + cot x) = 2

To Prove: sin 2x(tan x + cot x) = 2

Taking LHS,

sin 2x(tan x + cot x)

We know that,

sin 2x = 2 sinx cosx

= 2(sin²x + cos²x)

= 2 × 1 [∵ cos² θ + sin² θ = 1]

= 2

= RHS

∴ LHS = RHS

Hence Proved

cosec 2x + cot 2x = cot x

Prove that

cos 2x + 2sin²x = 1

Prove thatsin 2x(tan x + cot x) = 2