Chapter 7: Q.6 (page 473)

True or False: $\sin (- θ) + \sin (θ) = 0$ for any value of theta

Short Answer

Expert verified

Given statement is true statement

Step by step solution

Given information

We are given an trigonometric identity $\sin (- θ) + \sin (θ)$

Explanation for true statement

We know that sine is an odd function

Hence $\sin (- θ) = - \sin (θ)$

Hence we get,

$\sin (- θ) + \sin (θ) - \sin (θ) + \sin (θ) = 0$

For any value of theta

Explanation for false statement

Suppose

$\sin (- θ) + \sin (θ) \neq 0$

But sine is an odd function

hence $\sin (- θ) = - \sin (θ)$

Which is a contradiction to our assumption

Hence our assumption is wrong

And therefore

$\sin (- θ) + \sin (θ) - \sin (θ) + \sin (θ) = 0$

Conclusion

Given statement is true statement

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True or False: $\sin (- θ) + \sin (θ) = 0$ for any value of theta

Short Answer

Step by step solution

Given information

Explanation for true statement

Explanation for false statement

Conclusion

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True or False: sin-θ+sinθ=0for any value of theta

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

Decision Maths

Geometry

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

True or False: $\sin (- θ) + \sin (θ) = 0$ for any value of theta