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Question

If sinθ=35,cosϕ=1213 (where θ and ϕ both belongs to 1st quadrant), then which of the following is/are true?

A
cot(θ+ϕ)=6365
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B
tan(θ+ϕ)=5633
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C
sin(θ+ϕ)=5665
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D
cos(θϕ)=6365
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Solution

The correct options are
B tan(θ+ϕ)=5633
C sin(θ+ϕ)=5665
D cos(θϕ)=6365
sinθ=35cosθ=1sin2θ=45tanθ=34
Similarily
cosϕ=1213,sinϕ=513,tanϕ=512
tan(θ+ϕ)=tanθ+tanϕ1tanθtanϕ=34+512134×512=5633
sin(θ+ϕ)=sinθcosϕ+cosθsinϕ=5665
cos(θϕ)=cosθcosϕ+sinθsinϕ=6365

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