Question : If A is an acute angle and cot A + cosec A = 3, then the value of sin A is:
Option 1: $1$
Option 2: $\frac{3}{5}$
Option 3: $\frac{4}{5}$
Option 4: $0$
Correct Answer: $\frac{3}{5}$
Solution :
Given:
cot A + cosec A = 3.....................(1)
By using the identities: cosec
2
A – cot
2
A = 1
⇒ (cosec A + cot A) (cosec A – cot A) = 1
⇒ cosec A – cot A = $\frac{1}{3}$....................(2)
On adding both equations, we get:
⇒ 2cosec A = 3 + $\frac{1}{3}$ = $\frac{10}{3}$
⇒ cosec A = $\frac{10}{3×2}$ = $\frac{5}{3}$
⇒ sin A = $\frac{3}{5}$
Hence, the correct answer is $\frac{3}{5}$.
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