6.
If 3 sin 0 + 4 cos 0 = 5, find cot 0 + cosec e.
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ANSWER
Given, 3sinθ+4cosθ=5
3sinθ=5−4cosθ, squaring we get:
9sin
2
θ=25+16cos
2
θ−40cosθ
9(1−cos
2
θ)=25+16cos
2
θ−40cosθ(∵sin
2
θ=1−cos
2
θ)
9−9cos
2
θ=25+16cos
2
θ−40cosθ
⇒16cos
2
θ+9cos
2
θ−40cosθ+25−9=0
⇒25cos
2
θ−40cosθ+16=0
⇒(5cosθ−4)
2
=0
⇒5cosθ−4=0
⇒5cosθ=4
⇒cosθ=
5
4
cosecθ=
P
H
=
PQ
OP
=
3
5
cotθ=
P
B
=
PQ
OQ
=
3
4
Required Expression =cosecθ+cotθ
=
3
5
+
3
4
=
3
4
=
3
9
=3
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If 3 sin 0 + 4 cos 0 = 5, find cot 0 + cosec is 3
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