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:
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