Math, asked by sunnygampala22, 9 months ago

prove that root of secant squared theta + cosec and square theta is equal to tan theta + cot theta ​

Answers

Answered by Mankuthemonkey01
29

To Prove

\sf\sqrt{sec^2\theta + cosec^2\theta} = tan\theta + cot\theta

Solution

Taking LHS,

We know that

sec²∅ = tan²∅ + 1

and

cosec²∅ = cot²∅ + 1

So, replacing sec²∅ and cosec²∅, we get

\sf\sqrt{tan^2\theta + 1 + cot^2\theta + 1}

\sf\sqrt{tan^2\theta + cot^2\theta + 2}

Now,

2 can be written as 2 × 1

And, we know that 1 = tan∅cot∅

→ 2 = 2 tan∅cot∅

So we get

\sf\sqrt{tan^2\theta + cot^2\theta + 2tan\theta cot\theta}

Using a² + b² + 2ab = (a + b)²

\sf\sqrt{(tan\theta + cot\theta)^2}

= tan∅ + cot∅

Hence Proved

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