Question

prove (sec θ + tan θ) (1 – sin θ) = cos θ.

Answer 1

answer:step by step explanation

Answer 2

Step-by-step explanation:

LHS:

→ (sec θ + tan θ) (1 – sin θ)

→ (1/cos θ + sin θ/ cos θ) ( 1 - sin θ)

→ [(1 + sinθ)/cos θ] (1 – sin θ)

→ [(1 + sin θ) (1 – sin θ)] / cos θ

as we know ( a + b ) ( a – b ) = a² - b²

∴ ( 1² – sin² θ) / cos θ

$∵cos^{2}θ + sin^{2}θ = 1$

$∴1^{2} - sin^{2}θ = cos^{2}θ$

→ cos² θ /cos θ

→ cos θ = RHS