Question

Cosec x -sinx=m secx-cosx=n eliminate x?

Answer 1

Step 1:

The equation is .

Square on both sides.

.

Another equation is .

.

Step 2:

Add equation (1) and equation (2).

Apply Pythagorean identity .

Apply reciprocal identity and .

Step 3:

Multiply  and .

Square on both sides.

.

Step 4:

Subtract equation (3) from equation (4).

Solution:

.

Answer 2

m sinx=cos^2x, n cos x=sin^2x=(cos^2x/m)^2⇒cos^3x=m^2n   Simialrly, sin^3x=mn^2   (m^2n)^(2/3)+(mn^2)^(2/3)=1