First slide

Trigonometric Identities

Question

If $\sin θ + \cos θ = m$ and $\sec θ + \cos e c θ = n$ , then $n (m + 1) (m - 1) =$

Moderate

A

m
B

n
C

2m
D

2n

Solution

$m = \sin θ + \cos θ \Rightarrow m^{2} = 1 + 2 \sin θ \cos θ n = \frac{1}{\sin θ} + \frac{1}{\cos θ} = \frac{\sin θ + \cos θ}{\sin θ \cos θ} = \frac{m}{\frac{m^{2} - 1}{2}} c r o s s m u l p l i c a t i o n$

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