(D) Given expression: $(1-\cos \theta)(1+\cos \theta)$.Using the algebraic identity $(a-b)(a+b) = a^2 - b^2$,we have:$(1-\cos \theta)(1+\cos \theta) =

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(D) Given expression: $(1-\cos \theta)(1+\cos \theta)$.Using the algebraic identity $(a-b)(a+b) = a^2 - b^2$,we have:$(1-\cos \theta)(1+\cos \theta) = 1^2 - \cos^2 \theta = 1 - \cos^2 \theta$.According to the fundamental trigonometric identity $\sin^2 \theta + \cos^2 \theta = 1$,we can write $1 - \cos^2 \theta = \sin^2 \theta$.Therefore,the correct option is $D$.

Class 10 Mathematics Introduction to Trigonometry Mix Examples - Introduction to Trigonometry

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$(1-\cos \theta)(1+\cos \theta) = \dots$

A
$\operatorname{cosec}^{2} \theta$
B
$\cos ^{2} \theta$
C
$2-\cos ^{2} \theta$
D
$\sin ^{2} \theta$

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Introduction to Trigonometry

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Mix Examples - Introduction to Trigonometry

If $\sin 5 \theta = \cos 5 \theta$,then the value of $\theta$ is ..........

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Write 'True' or 'False' and justify your answer.
The value of $\sin \theta + \cos \theta$ is always greater than $1$.

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If $\sec 4A = \operatorname{cosec}(A - 20^\circ)$,where $4A$ is an acute angle,then the value of $A$ is $\ldots \ldots \ldots \ldots .$ (in $^\circ$)

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Which of the following is true for some $\theta$ (where,$0 < \theta < 90^{\circ}$)?

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$(1-\cos \theta)(1+\cos \theta) = \dots$

Similar Questions

If $\sin 5 \theta = \cos 5 \theta$,then the value of $\theta$ is ..........

Prove that $(\sin^{4} \theta - \cos^{4} \theta + 1) \operatorname{cosec}^{2} \theta = 2$.

Write 'True' or 'False' and justify your answer.The value of $\sin \theta + \cos \theta$ is always greater than $1$.

If $\sec 4A = \operatorname{cosec}(A - 20^\circ)$,where $4A$ is an acute angle,then the value of $A$ is $\ldots \ldots \ldots \ldots .$ (in $^\circ$)

Which of the following is true for some $\theta$ (where,$0 < \theta < 90^{\circ}$)?

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Write 'True' or 'False' and justify your answer.
The value of $\sin \theta + \cos \theta$ is always greater than $1$.