Question

7 sin theta - 24 cos theta = 0
Find the value of sec theta

Answer 1

Solution :-

→ 7sin θ - 24cos θ = 0

→ 7sin θ = 24cos θ

→ sin θ/cos θ = 24/7

using :-

• sin A / cos A = tan A in LHS,

→ tan θ = 24/7

using :-

• sec² A - tan² A = 1

→ sec² θ - (24/7)² = 1

→ sec² θ - (576/49) = 1

→ sec² θ = 1 + (576/49)

→ sec² θ = (49 + 576)/49

→ sec² θ = (625/49)

→ sec² θ = (25/7)²

square root both sides now,

→ sec θ = 25/7 (Ans.)

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