Question

Prove that
(sinA + cosecA)^2 + (cosA + secA)^2 = (1 + secA.cosecA)^2

Plz Answer this ASAP

Answer 1

Hey Buddy

Here's the answer

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# Some formulas

1. cos^2 A + sin^2 A = 1

2. sin A. cosec A = 1

3. cos A. sec A = 1

4. ( a + b )^2 = a^2 + b^2 + 2 a.b

Now

# L.H.S.

=> (sinA + cosecA)^2 + (cosA + secA)^2

=> Applying ( 4 )

=> ( Sin^2 A + cosec^2 A + 2 sin A.cosec A ) + ( cos^2 A + sec^2 A + 2cos A. sec A )

=> sin^2 A + cosec^2 A + 2(1) + cos^2 A + sec^2 A + 2(1)

=> sin^2 A + cos^2 A + cosec^2 A + sec^2 A + 4

=> 1 + cosec^2 A + sec^2 A + 4

=> 5 + cosec^2 A + sec^2 A

=> 5 + ( 1/sin^2 A ) + ( 1 / cos^2 A )

=> taking L.C.M.

=> 5 + ( cos^2 A + sin^2 A )/(sin A. cos A )^2

=> 5 + 1/(sin A. cos A )^2

=> 5 + ( cosec A. sec A )^2

HOPE HELPED...

JAI HIND

:)