33. If (sin + cos 0) = 3 then prove that tan 6+cot e = 1. Or, Find the value of the expression given below. cos (45° +8) + cos (45° - ) +(cot 30° + sin 90°)(tan 60° - sec 0°). tan (60° +8). tan (30°-O) -
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Answer:
sinθ+cosθ=
3
=(sinθ+cosθ)
2
=3
=sin
2
θ+cos
2
θ+2sinθcosθ=3
⇒2sinθcosθ=2
⇒sinθcosθ=1
⇒sinθcosθ=sin
2
θ+cos
2
θ
⇒1=
sinθcosθ
sin
2
θ+cos
2
θ
⇒tanθ+cotθ=1
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