Question

prove that tan theta + cot theta= sec theta × cosec theta​

Answer 1

Answer:

cotθ+tanθ=cosecθ×secθ

Answer:

cot\theta + tan\theta = cosec \theta \times sec \thetacotθ+tanθ=cosecθ×secθ

LHS is

Cot \theta + tan \theta= \frac {cos \theta }{sin \theta }+ \frac {sin \theta }{ cos \theta }Cotθ+tanθ=

sinθ

cosθ

+

cosθ

sinθ

= \frac {cos^{2} \theta + sin^{2} \theta}{ sin \theta \times cos \theta}=

sinθ×cosθ

cos

2

θ+sin

2

θ

Therefore cos^{2} \theta + sin^{2} \theta = 1cos

2

θ+sin

2

θ=1

= \frac {1}{ sin \theta \times cos \theta}=

sinθ×cosθ

1

= \frac {1}{ sin \theta} \times \frac {1}{ cos \theta}=

sinθ

1

×

cosθ

1

Therefore,

cot \theta +tan \theta =cosec \theta \times sec \thetacotθ+tanθ=cosecθ×secθ

Hence proved.

Answer 2

Answer:

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