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OTP to be sent to Change
SinA + CosA = p
SecA + CosecA = q
Now, p2 - 1
= (SinA + CosA)2 - 1
= (Sin2A + 2SinACosA + Cos2A) - 1
= [ (Sin2A+Cos2A) + 2SinACosA ] - 1
= [ 1 + 2SinACosA ] - 1
= 2SinACosA [Equation (i)]
So, q(p2 - 1)
= (SecA + CosecA)*(2SinACosA) [from Equation (i)]
= SecA*(2SinACosA) + CosecA*(2SinACosA)
= (1/CosA)*(2SinACosA) + (1/SinA)*(2SinACosA)
= 2SinA + 2CosA
= 2(SinA + CosA)
= 2p
Regards
Arun (askIITians forum expert)
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