SSC MTS Model Paper 1

Question : 27 of 150

Marks: +1, -0

If sinθ + cosθ = p and secθ + cosecθ = q, then find the value of q(p

^{2}

– 1).

Solution:

q ( p ^ { 2 } - 1 \ ) = ( \sec θ + \cosec θ ) { ( \sin θ + \cos \θ ) ^ { 2 } - 1 \}

= ( { 1 } /{ \cos θ } + { 1 }/ { \sin θ } \) \{ \sin ^ { 2 } θa + \cos ^ { 2 } θ + 2 \sin \θ \cos θ - 1 \}

=( { \sin θ + \cos θ }/ { \cos θ \sin θ } ) ( 1 + 2 \sinθ \cos θ - 1 )

=( { \sinθ + \cos θ } /{ \cos θ \sin θ } ) ( 2 \sin θ \cos θ )

= 2 ( \sin θ + \cos θ ) = 2 { p }

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