Answer:
15. Option A is correct
16. Option B is correct.
Explanation:
Question 5:
sin2Ф = 2sinФcosФ
We are given sinФ = 9/13
and we need to find cosФ in order to find sin2Ф
We know that sin^2Ф + cos^2Ф= 1
so, cos^2Ф = 1- sin^2Ф
cos^2Ф = 1- (9/13)^2
cos^2Ф = 88/169
taking √ on both sides:
√cos^2Ф = √88/169
cosФ = (2√22)/13
Now
sin2Ф = 2sinФcosФ
= 2 (9/13) (( 2√22)/13)
sin 2Ф = 36√22 / 169
Now we find cos2Ф
The formula for cos2Ф = cos^2Ф - sin^2Ф
cos2Ф = ((2√22)/13)^2 - (9/13)^2
cos2Ф = 4*22 /169 - 81/169
cos2Ф = 7/169
So, Option A is correct
Question No 6
We need to find sin2Ф and cos2Ф where cosФ = 6/13
We are given cosФ = 6/13
and we need to find sinФ in order to find sin2Ф and cos2Ф
We know that sin^2Ф + cos^2Ф= 1
so, sin^2Ф = 1- cos^2Ф
sin^2Ф = 1- (6/13)^2
sin^2Ф = 133/169
taking √ on both sides:
√sin^2Ф = √133/169
sinФ = √133/13
Now
sin2Ф = 2sinФcosФ
= 2 (√133/13) (6/13)
sin2Ф = 12√133 / 169
Now we find cos2Ф
The formula for cos2Ф = cos^2Ф - sin^2Ф
cos2Ф = (6/13)^2 - (√133/13)^2
cos2Ф = 36/169 - (133/169)
cos2Ф = -97/169
Since the quadrant is 1st so, cos2Ф will be Positive i.e. 97/169
cos2Ф = 97/169
So, Option B is correct.