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If sinA + sin2A = 1 then what is the value of cos2A + cos4A?
- A½
- B1
- C2
- D3
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0
CCommunity
Given,
sinA + sin2A = 1
⇒ sinA = 1 – sin2A = cos2A ----(1) (? sin2θ + cos2θ = 1)
Squaring on both sides
sin2A = cos4A ----(2)
Substitute (1) and (2) in the given expression.
cos2A + cos4A = sinA + sin2A = 1
∴ cos2A + cos4A = 1
sinA + sin2A = 1
⇒ sinA = 1 – sin2A = cos2A ----(1) (? sin2θ + cos2θ = 1)
Squaring on both sides
sin2A = cos4A ----(2)
Substitute (1) and (2) in the given expression.
cos2A + cos4A = sinA + sin2A = 1
∴ cos2A + cos4A = 1
0
CCommunity
Given,
sinA + sin2A = 1
⇒ sinA = 1 – sin2A = cos2A ----(1) (? sin2θ + cos2θ = 1)
Squaring on both sides
sin2A = cos4A ----(2)
Substitute (1) and (2) in the given expression.
cos2A + cos4A = sinA + sin2A = 1
∴ cos2A + cos4A = 1
sinA + sin2A = 1
⇒ sinA = 1 – sin2A = cos2A ----(1) (? sin2θ + cos2θ = 1)
Squaring on both sides
sin2A = cos4A ----(2)
Substitute (1) and (2) in the given expression.
cos2A + cos4A = sinA + sin2A = 1
∴ cos2A + cos4A = 1