The value of (\sin 37^{\circ} \cos 53^{\circ}+\cos 37^{\circ} \sin 53^{\circ}) - {4 \cos ^{2} 37^{\circ}-7+4 \cos ^{2} 53^{\circ}}/{\tan ^{2} 47^{\circ}+4-cosec^{2} 43^{\circ}} is

SSC CGL 18 Aug 2021 Shift 2 Paper

Question : 60 of 100

Marks: +1, -0

The value of

(\sin 37^{∘} \cos 53^{∘}+\cos 37^{∘} \sin 53^{∘})

-\;{4 \cos ^{2} 37^{∘}-7+4 \cos ^{2} 53^{∘}}/{\tan ^{2} 47^{∘}+4-cosec^{2} 43^{∘}}

Solution:

[\sin 37^{∘} \cos 53^{∘}+\cos 37^{∘} \sin 53^{∘}

-\;{4 \cos ^{2} 37^{∘}-7+4 \cos ^{2} 53^{∘}}/{\tan ^{2} 47^{∘}+4-cosec^{2} 43^{∘}}]

=[\sin (90^{∘}-53^{∘}) \cos 53^{∘}

+\cos (90^{∘}-53^{∘})

\sin 53^{∘}-\;{4 \cos ^{2}(90^{∘}-53^{∘})+4 \cos ^{2} 53^{∘}-7}/{\tan ^{2}(90^{∘}-43^{∘})-cosec^{2} 43^{∘}+4}]

\;\; =[\cos ^{2} 53^{∘}+\sin ^{2} 53^{∘}

-\;{4(\sin ^{2} 53^{∘}+\cos ^{2} 53^{∘})-7}/{\cot ^{2} 43^{∘}-cosec^{2} 43^{∘}+4}]

\;\; =1-\;{4(1)-7}/{-[cosec^{2} 43^{∘}-\cot ^{2} 43^{∘}]+4}

\;\; =1-\;{(-3)}/{4-1}=1+\;{3}/{3}=1+1=2

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