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Q12 of 164 Page 41

If prove that 1–2 sin²A = 2cos²A – 1.

Let the third side be p,

By Pythagoras theorem,

⇒ 8² + p² = 17²

⇒ 64 + p² = 289

⇒ p² = 225

⇒ p = 15

Therefore, the other angles are:

sin θ =

cos θ =

Putting these values in the left hand side:
⇒ 1–2×

⇒ 1–2×

⇒ 1–

⇒

Putting values in the right hand side:

⇒ 2×

⇒ 2× –1

⇒

⇒

Therefore, Left hand side and right hand side are equal.

Hence proved.

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11

If show that

12

If prove that 1–2 sin²A = 2cos²A – 1.

13

Evaluate.

(i) sin 45° + cos 45°

(ii) sin 60° tan 30°

(iii)

(iv) cos²60° sin²30° + tan² 30° cot² 60°

(v) 6cos² 90° + 3sin² 90° + 4 tan² 45°

(vi)

(vii)

(viii) 4(sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°)

13

Evaluate.

(i) sin 45° + cos 45°

(ii) sin 60° tan 30°

(iii)

(iv) cos²60° sin²30° + tan² 30° cot² 60°

(v) 6cos² 90° + 3sin² 90° + 4 tan² 45°

(vi)

(vii)

(viii) 4(sin⁴ 30° + cos⁴ 60°) – 3 (cos² 45° – sin² 90°)