Q. 1 D4.6( 17 Votes )

# Evaluate the following.

D. 2tan^{2} 45° + cos^{2} 30° - sin^{2} 60°

Answer :

By trigonometric identities,

sin 60° = √3/2

tan 45° = 1

cos 30° = √3/2

Putting these values in 2 tan^{2} 45° + cos^{2} 30° - sin^{2} 60°, we get

2 tan^{2} 45° + cos^{2} 30° - sin^{2} 60° = 2(1)^{2} + (√3/2)^{2} – (√3/2)^{2}

⇒ 2 tan^{2} 45° + cos^{2} 30° - sin^{2} 60° = 2

Thus, 2 tan^{2} 45° + cos^{2} 30° - sin^{2} 60° = 2.

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