Q9 of 120 Page 95

If tan θ =1, then find the value of sin2 θ -cos2 θ.

Given: √3 tan θ = 1

⇒ tan θ = 1/√3


⇒ θ = tan-1 (1/√3) [Taking tan inverse]


⇒ θ = 30°


To find value of sin2 θ – cos2 θ, substitute value of θ


We get, sin2 30° - cos230°


= (1/2)2 – (√3/2)2


= 1/4 - 3/4


= -2/4 = -1/2


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