First slide

Trigonometric Identities

Question

If $\sin θ + \cos e c θ = 2,$ then $\sin^{2} θ + \cos e c^{2} θ$ is equal to

Moderate

A

1
B

4
C

2
D

none

Solution

$\sin θ + \cos e c θ = 2 \Rightarrow \sin θ + \frac{1}{\sin θ} = 2 \Rightarrow {(\sin θ - 1)}^{2} = 0 \Rightarrow \sin θ = 1 \Rightarrow \cos e c θ = 1 ∴ \sin^{2} θ + \cos e c^{2} θ = 1 + 1 = 2$

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