SSC MTS Model Paper 3

Question : 38 of 150

Marks: +1, -0

Find the value of θ [0° < θ < 90°] for which

{ \cos θ }/ { 1 - \sin θ } + { \cos θ } /{ 1 + \sin θ } = 4

Solution:

{ \cos θ} /{ 1 - \sin θ} + { \cos \θ}/ { 1 + \sin θ} = 4

{ \cos θ ( 1 + \sin θ + 1 - \sin θ ) }/ { 1 - \sin ^ { 2 } θ } = 4

{ \cos θ ×2 } /{ \cos ^ { 2 } θ } = 4 ⇒ { 2 }/ { \cos θ } = { 4 } /{ 1 }

⇒\cos θ = \cos 60 ^ { ° } ⇒ θ = 60 ^ { ° }

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