Question

Evaluate: (1+cot^2)(sin^2 theta)

Answer 1

(1+cot^2 theta)sin^2theta

We know cot theta = cos theta / sin theta

=>(1+cos^2theta/sin^2 theta)sin^2theta

Inside the bracket taking sin^2theta as LCM

=>((sin^2theta+cos^2theta)/sin^2theta)sin^2theta

We know sin^2theta + cos^2theta = 1

=>1/sin^2theta×sin^2theta

sin^2theta cancels

=>1 is your answer

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Answer 2

Answer:

1

Step-by-step explanation:

• ( 1+cot² theta)(sin² theta)
• ( cosec² theta)(1/cosec²theta)

(since: 1+cot² theta = cosec² theta

sin²theta = 1/ cosec² theta )

( cosec²theta. cosec²theta gets cancelled)

• 1×1=1