SSC CGL 26 Oct 2014 Shift 2 Paper

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Question : 141 of 200

Marks: +1, -0

If sin θ =

3/5

, then the value of

{tanθ + cosθ}/{cotθ+cosecθ}

is equal to

${29}/{60}$
${31}/{60}$
${34}/{60}$
${37}/{60}$

Solution:

sin θ =

3/5

∴ cos θ =

√{1-sin^2 θ}

=

√{1-(3/5)^2}

=

√{1-9/{25}}

=

√{{16}/{25}}

=

4/5

tan θ =

{sinθ}/{cosθ}

=

{3/5}/{4/5}

=

3/4

cot θ =

1/{tanθ}

=

4/3

cosec θ =

1/{sinθ}

=

5/3

∴

{tanθ + cosθ}/{cotθ+cosecθ}

=

{3/4+4/5}/*{4/3+5/3}

=

{{15+16}/{20}}/{{4+5}/3}

=

{31}/{20}

×

3/9

=

{31}/{60}

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