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`        sin theta +cos theta =p and secsquare theta +cosec square theta =q then prove that q(p square -1) =2p`
2 years ago

```							SinA + CosA = pSecA + CosecA = qNow, 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 RegardsArun (askIITians forum expert)
```
2 years ago
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