The value of 11 cot²θ - 11 cosec²θ is :
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Answer:
\frac{11}{cot^2\theta}-\frac{11}{cos^2\theta}
cot
2
θ
11
−
cos
2
θ
11
=11(\frac{1}{cot^2\theta})-11(\frac{1}{cos^2\theta})=11(
cot
2
θ
1
)−11(
cos
2
θ
1
)
=11tan^2\theta-11sec^2\theta=11tan
2
θ−11sec
2
θ
=11(tan^2\theta-sec^2\theta)=11(tan
2
θ−sec
2
θ)
=-11(sec^2\theta-tan^2\theta)=−11(sec
2
θ−tan
2
θ)
\text{using}using
\boxed{\bf\,sec^2\theta-tan^2\theta=1}
sec
2
θ−tan
2
θ=1
\text{we get}we get
=11(1)=11(1)
=-11=−11
\implies\boxed{\bf\,11(\frac{11}{cot^2\theta})-(\frac{11}{cos^2\theta})=-11}⟹
11(
cot
2
θ
11
)−(
cos
2
θ
11
)=−11
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