simplify (1-cos^2 theta)(1+cot^2 theta) ?

-aliya

please help, show me steps ??

cidyah

(1-cos^2 theta)(1+cot^2 theta)=

sin^2(theta) csc^2(theta)

= sin^2(theta) / sin^2(theta) = 1

anonymous

Note that 1- cos^2(theta) = sin^2(theta)

Note that 1 + cot^2(theta) = 1 + cos^2(theta)/sin^2(theta)

= 1/sin^2(theta)

Hence (1-cos^2 theta)(1+cot^2 theta)

= sin^2(theta) * 1/sin^2(theta)

= 1

sahsjing

(1-cos^2 theta)(1+cot^2 theta)

= sin^2 theta csc^2 theta

= 1

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Attn: sinx cscx = 1