Q.17 If A+B 90 prove thattanA tanB + tanA cotB sin2 Bcos2AtanAsinA sec

1.	Q.17 If A+B 90 prove thattanA tanB + tanA cotB sin2 Bcos2AtanAsinA secA
Answer» Given, LHS = root tan a tan b + tan a cot b/sin a sec b - sin^2 b/cos^2 a = root tan a tan(90-a) + tan a cot(90-a)/sin a sec(90-a) - sin^2(90-a)/cos^2 a = root tan a.cot a + tan a.tana/sin a.cosec a - cos^2 a/cos^2 a = root 1+tan^2 a/1 - 1 = root tan^2 a = tan a.

Q.17 If A+B 90 prove thattanA tanB + tanA cotB sin2 Bcos2AtanAsinA secA

Answer»

Given, LHS = root tan a tan b + tan a cot b/sin a sec b - sin^2 b/cos^2 a

= root tan a tan(90-a) + tan a cot(90-a)/sin a sec(90-a) - sin^2(90-a)/cos^2 a

= root tan a.cot a + tan a.tana/sin a.cosec a - cos^2 a/cos^2 a

= root 1+tan^2 a/1 - 1

= root tan^2 a

= tan a.