The numerical value of 1 - cos x1 - cos x1 - 2x is

Given, (1 cos x)(1 + cos x)(1 + ^2x) using (A+B)(A B)=A^2 B^2 and (cosec^2x ^2x)=1 ⇒ (1 nbsp; cos^2x)(cosec^2 x) Now, using (sin^2x+cos ^2x)=1 ⇒sin^2x ...

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Standard XIII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

The numerical...

Question

The numerical value of $(1 - cos x) (1 + cos x) (1 + {cot}^{2} x)$ is

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Solution

The correct option is B $1$
Given, $(1 - cos x) (1 + cos x) (1 + {cot}^{2} x)$

$using (A + B) (A - B) = A^{2} - B^{2}$
and $({cosec}^{2} x - {cot}^{2} x) = 1$

$\Rightarrow (1 - {cos}^{2} x) ({cosec}^{2} x)$

Now, using $({sin}^{2} x + {cos}^{2} x) = 1$

$\Rightarrow {sin}^{2} x . {cosec}^{2} x = 1$

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Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Standard XIII Mathematics

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The numerical value of (1−cosx)(1+cosx)(1+cot2x) is

The correct option is B 1Given, (1−cosx)(1+cosx)(1+cot2x) using (A+B)(A−B)=A2−B2 and (cosec2x−cot2x)=1 ⇒(1−cos2x)(cosec2x) Now, using (sin2x+cos2x)=1 ⇒sin2x.cosec2x=1

The numerical value of $(1 - cos x) (1 + cos x) (1 + {cot}^{2} x)$ is