Question

please solve this question...............................................................

Answer 1

Angles are written as A and B

Answer:

Proved below.

Step-by-step explanation:

From the properties of trigonometric ratios :

        sin^2 A + cos^2 A = 1    ⇒ - sin^2 A = cos^2 A - 1

       1 + tan^2 B = sec^2 B

       secB = 1 / cosB

Given, here,

⇒ cos^2 A - sin^2 A = tan^2 B

⇒ cos^2 + cos^2 A - 1 = tan^2 B           { from above }

⇒ 2 cos^2 A - 1 = tan^2 B

⇒ 2 cos^2 A = tan^2 B + 1

⇒ 2 cos^2 A = sec^2 B

⇒ √2 cosA = secB        { sq. root on both sides}

⇒ √2 cosA = 1 / cosB

⇒ cosB = 1 / ( √2 cosA )  

           LHS = RHS, as required.

       Proved.