Topics
Trig Fns - Identities
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India
Class XI

Applications of angle sum and difference identities

Lesson
Practice

Interactive practice questions

By using the expansion of $\cos\left(A+B\right)$cos(A+B), verify $\cos2x=2\cos^2\left(x\right)-1$cos2x=2cos2(x)−1.

Easy
4min

By using the expansion of $\sin\left(A+B\right)$sin(A+B), verify that $\sin2x=2\sin x\cos x$sin2x=2sinxcosx.

Easy
1min

By simplifying the left hand side (LHS) of the identity, verify that $\sin\left(x+y\right)-\sin\left(x-y\right)=2\cos x\sin y$sin(x+y)−sin(x−y)=2cosxsiny.

Easy
2min

By simplifying the left hand side of the identity, verify that $\frac{\sin\left(x-y\right)}{\cos x\cos y}=\tan x-\tan y$sin(x−y)cosxcosy​=tanx−tany

Easy
3min
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Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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