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Question

If 3sinθ+4cosθ=5, then find cotθ+cosecθ

A
1
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B
-1
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C
3
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D
2
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Solution

The correct option is B 3
Given, 3sinθ+4cosθ=5
3sinθ=54cosθ, squaring we get:
9sin2θ=25+16cos2θ40cosθ
9(1cos2θ)=25+16cos2θ40cosθ(sin2θ=1cos2θ)
99cos2θ=25+16cos2θ40cosθ
16cos2θ+9cos2θ40cosθ+259=0
25cos2θ40cosθ+16=0
(5cosθ4)2=0
5cosθ4=0
5cosθ=4
cosθ=45
cosecθ=HP=OPPQ=53
cotθ=BP=OQPQ=43
Required Expression =cosecθ+cotθ
=53+43=43=93=3
222821_235591_ans.png

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