If \sec (5 \alpha-15^{\circ})=cosec(15^{\circ}-2 \alpha) then the value of \cos \alpha+\sin 2 \alpha+\tan (1.5 \alpha) is

SSC CGL 20 Aug 2021 Shift 1 Paper

Question : 55 of 100

Marks: +1, -0

\sec (5 α-15^{∘})=cosec(15^{∘}-2 α)

then the value of

\cos α+\sin 2 α+\tan (1.5 α)

Solution:

Given,

\sec (5 α-15^{∘})=cosec(15^{∘}-2 α)

⇒ \sec (5 α-15^{∘})

=\sec [90^{∘}-(15^{∘}-2 α)]

[ ∵ \sec (90^{∘}-θ)=cosec θ]

⇒ 5 α-15^{∘}=90^{∘}-15^{∘}+2 α

⇒ \;\; 3 α=90^{∘}

⇒ \;\; α=30^{∘}

∴ \cos α+\sin 2 α+\tan (1.5 α)

=\cos 30^{∘}+\sin 60^{∘}+\tan 45^{∘}

=\;{√{3}}/{2}+\;{√{3}}/{2}+1

=2(\;{√{3}}/{2})+1=(√{3}+1)

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