# Show that:

To prove:

Let, y =

we can say that, we have to prove: tan y =

2y =

sin 2y = 3/4

As we know that: sin 2y =

8 tan y = 3 + 3 tan2y

3 tan2y – 8tan y + 3 = 0

tan y =

tan y =

tan y = or tan y =

Hence, tan y =

OR

Given:

We have to solve for x.

Let, y =

x = tan y

LHS = cos y =

As, RHS =

Let, cot-1(3/4) = θ

cot θ = 3/4

sin θ =

RHS = sin θ = 4/5

As, LHS = RHS {given}

5 = 4√(1+x2)

Squaring both sides, we have-

25 = 16(1+x2)

25 = 16 + 16x2

9 = 16x2

x2 = 9/16

x = ±√(9/16) = ±3/4

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