Question

if a+b =90 degree then prove that ( tan A*tanB +tan A* cot B÷sinA *sec B ) - (sin ^2÷cos ^2 B )​

Answer 1

Answer:Look below

Step-by-step explanation:

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.

Hope this helps!

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