Question

when each term of sin2 + cos2 = 1 is divided by sin2 what will be the result?​

Answer 1

Step-by-step explanation:

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Answer 2

$cosec^{2}\theta-cot^{2}\theta=1$

Given data:

The expression $sin^{2}\theta+cos^{2}\theta=1$

To find:

A mathematical result when each term of $sin^{2}\theta+cos^{2}\theta=1$ is divided by $sin^{2}\theta$

Step-by-step explanation:

The given expression is $sin^{2}\theta+cos^{2}\theta=1$

• First term ( when divided by $sin^{2}\theta$ )

= $\dfrac{sin^{2}\theta}{sin^{2}\theta}$

= 1

• Second term ( when divided by $sin^{2}\theta$ )

= $\dfrac{cos^{2}\theta}{sin^{2}\theta}$

= $cot^{2}\theta$

• Third term ( when divided by $sin^{2}\theta$ )

= $\dfrac{1}{sin^{2}\theta}$

= $cosec^{2}\theta$

Combining the terms, we can write

$1+cot^{2}\theta=cosec^{2}\theta$

⇒ $cosec^{2}\theta-cot^{2}\theta=1$

This is an Trigonometric identity.

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