Question

tan square theta + cot square theta = sec sqaure theta multiply cosec square theta - 2​

Answer 1

Solution:

To prove: tan²β+cot²β = sec²βcosec²β-2 or 2+tan²β+cot²β = sec²βcosec²β

Taking L.H.S.,

= tan²β+cot²β+2

= tan²β+1+cot²β+2.tanβ.cotβ              (∴tanβ.cotβ = 1)

= (tanβ+cotβ)²

= $(\frac{sin\beta}{cos\beta}+\frac{cos\beta}{sin\beta})^{2}$

= $(\frac{sin^{2}\beta+cos^{2}\beta}{sin\beta.cos\beta})^{2}$

= $(\frac{1}{sin\beta.cos\beta})^{2}$

= (cosecβ.secβ)²

= sec²β.cosec²β

Hence Proved

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