SSC MTS Model Paper 1

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Question : 40 of 150

Marks: +1, -0

If

{ \cos α } /{ \cos β } = m

and

{ \cos α } /{ \sin β }=n

, then find the value of (m

^{2}

+ n

^{2}

) cos

^{2}

β.

n
2n
n $^{2}$
2n $^{2}$

Solution:

( { m } ^ { 2 } + { n } ^ { 2 } ) \cos ^ { 2 } β

= ( { \cos ^ { 2 } α }/ { \cos ^ { 2 } β } + { \cos ^ { 2 } α }/ { \sin ^ { 2 } β } ) \cos ^ { 2 }β

( ∵ { m } = { \cos α } /{ \cos β }

and

n = { \cos α } / {\sin β } )

= ( { \cos ^ { 2 } α\sin ^ { 2 } β + \cos ^ { 2 } α \cos ^ { 2 } β } /{ \cos ^ { 2 } β \sin ^ { 2 } β} ) \cos ^ { 2 } β

= {\cos ^ { 2 } α}({\sin ^ { 2 } β + \cos ^ { 2 } β } /{ \cos ^ { 2 } β \sin ^ { 2 } β}) \cos ^ { 2 } β

= {\cos ^ { 2 } α}(1/{ \cos ^ { 2 } β \sin ^ { 2 } β}) \cos ^ { 2 } β

= {\cos ^ { 2 } α}/{\sin ^ { 2 }β}

= ({\cos α}/{\sin β})^ { 2 }= n^2

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