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Given sine of x equals negative 5 over 13 and cos x > 0, what is the exact solution of cos 2x?

Given Sine Of X Equals Negative 5 Over 13 And Cos X Gt 0 What Is The Exact Solution Of Cos 2x class=

Sagot :

The value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given:

sinx = -5/13

and cosx > 0

We know,

cos2x = 1 - 2sin²x

sinx = -5/13

Squaring on both sides:

sin²x = 25/169

Multiply by 2 on both the sides:

2sin²x = 2(25/169)

Add -1 on both sides:

-1 + 2sin²x = -1 + 2(25/169)

or

1 - 2sin²x = 1 - 2(25/169)

cos2x = 1 - 50/169

cos2x = 119/169    (as the cosx > 0)

Thus, the value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

Learn more about trigonometry here:

brainly.com/question/26719838

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