Math, asked by k3ishe7risharsh, 1 year ago

Sin 2 A+cos 2 B+sec 2 C=tan 2 D given:sinA=cosB

Answers

Answered by kvnmurty
2
Given  sin A = cos B  = sin(π/2 - B)
 =>  A + B = π/2
Since A, B, C and D are angles of a quadrilateral. So
angles C+ D = 3π/2
=>  cos (C+D) = 0
=> cos C cos D = sin C sin D
=>  tan C = Cot D     (1)

LHS = sin² A + cos² B + sec² C
    = 2 sin² A + tan² C + 1
    = 2 sin² A + Cot² D + 1   using (1)

This expression can be simplified only if there is a relation between the angles A and D.
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