RRB NTPC Mains or Stage 2 Model Paper 7 with solutions

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Question : 18 of 120

Marks: +1, -0

If tan q = 1, then find the value of

{8sinθ +5sin θ}/{sin^3θ- 2cos^3θ+ 7cos θ}

2
$2 1/ 2$
3
$4/5$

Solution:

(a) tan θ = 1
sec θ=

√{1+ tan^2 θ} = √{1+1} = √2

cos θ

=1/√2

sinθ=

{1- cos^2 θ}

=√{1-[1/√2]^2}=1/√2

NOW,

{8sinθ+5sinθ}/{sin^3θ-2 cos^3θ+ 7 cosθ}

{8×1/√+5×1/√2}/{[1/√2]^3-2×[1/√2]^3+7×1/√2}

={{8+5}/√2}/{1/2√2-2/2√2+7/√2}={(8+5)/√2}/{1-2+14/{2√2}}

={13×2}/13=32

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