Question

If tan x=3\4,then value of cos2x is
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Answer 1

sec²x - tan²x = 1

sec²x = 1 + tan²x

sec²x = 1 + (3/4)²

sec x = √ 1 + 9/16

sec x = √25/9

sec x = 5/3

cos x = 3/5

cos 2x = 2cos²x - 1

= 2 (9/25) - 1

= 18/25 - 1

= 18 - 25/ 25

= -7/25

Answer 2

Given:

tan x=3/4

To Find:

value of cos2x

Solution:

We know that,

sec²x - tan²x = 1

sec²x = 1 + tan²x

sec²x = 1 + (3/4)²

sec x = √ 1 + 9/16

sec x = √25/9

sec x = 5/3

So,

cos x = 3/5

Also,

cos 2x = 2cos²x - 1

           = 2 (9/25) - 1

           = 18/25 - 1

           = 18 - 25/ 25

            = -7/25

Hence, the value of cos2x is -7/25.