Chapter 7: Q.1 (page 473)

True or False: $\sin^{2} (θ) = 1 - \cos^{2} (θ)$

Short Answer

Expert verified

The given identity is true

Step by step solution

Given information

We are given a identity $\sin^{2} (θ) = 1 - \cos^{2} (θ)$

Explanation for true statement

We know a trigonometric identity

$\sin^{2} (θ) + \cos^{2} (θ) = 1$

on rearranging the identity we get,

$\sin^{2} (θ) = 1 - \cos^{2} (θ)$

Hence the given identity is true

Explanation for false statement

Consider that the given identity is false

Hence,

$\sin^{2} (θ) \neq 1 - \cos^{2} (θ)$

And therefore

$\sin^{2} (θ) + \cos^{2} (θ) \neq 1$

Which is false.

Conclusion

The given statement is true statement

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True or False: $\sin^{2} (θ) = 1 - \cos^{2} (θ)$

Short Answer

Step by step solution

Given information

Explanation for true statement

Explanation for false statement

Conclusion

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True or False:sin2θ=1-cos2θ

Short Answer

Step by step solution

Given information

Explanation for true statement

Explanation for false statement

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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True or False: $\sin^{2} (θ) = 1 - \cos^{2} (θ)$