If cotθ = 28/45, then find the value of (sinθ - cosθ).
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 17/53.
cotθ = 28/45 = B/P
By Pythagoras theorem,
⇒ H2 = B2 + P2
here, H = Hypotaneous, B = Base, and P = Perpendicular
Now,
⇒ H2 = 282 + 452
⇒ H2 = 784 + 2025
⇒ H2 = 2809
⇒ H = 53
So, the value of (sinθ - cosθ)
⇒ (P/B - B/H)
⇒ (45/53 - 28/53)
⇒ (45 - 28)/53
⇒ 17/53
So, the value of (sinθ - cosθ) is 17/53