Math, asked by csraofeb76821, 3 months ago

tan(90-theta)+cot(90-theta)=cosec(theta)*sec(theta)

Answers

Answered by sharanyalanka7
35

Answer:

Step-by-step explanation:

To Prove :-

tan(90^{\circ}-\theta)+cot(90^{\circ}-\theta) = csc\theta\times sec\theta

Solution :-

Taking L.H.S :-

= tan(90^{\circ}-\theta)+cot(90^{\circ}-\theta)

We know that :-

1) tan(90^{\circ}-\theta) = cot\theta

2)cot(90^{\circ}-\theta)=tan\theta

=cot\theta+tan\theta

=\dfrac{cos\theta}{sin\theta}+\dfrac{sin\theta}{cos\theta}

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

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

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

=sec\theta\times csc\theta

=csc\theta\times sec\theta

= R.H.S

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