Prove that A mathematical identity to prove, equating an expression with inverse tangent to an expression with inverse cosine: 2 tan⁻¹ (sqrt((a - b) / (a + b)) tan(θ/2)) = cos⁻¹ ((a cos θ + b) / (a + b cos θ)).

Q9 of 303 Page 4

Prove that

Given:-

Take

LHS

We know that, Formula

Thus,

Dividing numerator and denominator by , we get

We know that, Formula

Thus,

= RHS

So,

Hence Proved

Solve the following equations for x:

prove that:

, where a= ax – by and β=ay+bx.

For any a,b,x,y>0, prove that:

, where a=-ax by, β = bx + ay.