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NDA Math Trigonometric Ratios of Angles and Equations
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© examsnet.com
Question : 7
Total: 100
If sin α +cos α=p , then what is cos
2
(2α ) equal to?
[NDA I 2019]
p
2
p
2
−1
p
2
|2−p
2
|
p
2
+1
Validate
Solution:
(C)
Given
sin α + cosα = p
(sin α + cosα )
2
= p
2
1 + sin2α = p
2
sin 2α = p
2
− 1
cos
2
(2α ) = 1 − sin
2
2α
= 1 − ( p
2
− 1)
2
= 1−( p
4
− 2 p
2
+ 1)
= 2 p
2
− p
4
∴ cos
2
(2α ) = p
2
(2−p
2
)
© examsnet.com
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