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Question
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Options
1
`1/2`
2
3
Solution
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is 1.
Explanation:
Given,
sinA + sin2A = 1
⇒ sinA = 1 – sin2A = cos2A ...[∵ sin2θ + cos2θ = 1]
On squaring both sides, we get
sin2A = cos4A
⇒ 1 – cos2A = cos4A
⇒ cos2A + cos4A = 1
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