Try the other way
If 3 cot θ = 5 , then find the value of
5 sin θ + 3 cos θ 5 sin θ − 3 cos θ
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2 solutions
3 cot θ = 5 5 sin θ + 3 cos θ 5 sin θ − 3 cos θ = sin θ 5 sin θ + 3 cos θ sin θ 5 sin θ − 3 cos θ = 5 + 3 cot θ 5 − 3 cot θ = 5 + 5 5 − 5 = 1 0 0 = 0
Since sin and cos are functions like ln (\ln), (\sqrt ), ∫ (\int) and lim (\lim). you should put a backslash in front sin (\sin) and cos (\cos). Note that they are not italic which is for valuables such as x , y , z , d x , d y , d z , θ . Note that they are italic like in your solution without the backslash s i n (sin) and c o s (cos).
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Ok. will follow it from next time
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I have done the changes for your solution above.
3 c o t θ = 5 . So s i n θ 3 c o s θ = 5 ⇒ 3 c o s θ = 5 s i n θ .
Substitute this in the question, 5 s i n θ + 3 c o s θ 5 s i n θ − 3 c o s θ = 5 s i n θ + 5 s i n θ 5 s i n θ − 5 s i n θ = 0 .