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°)

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Philoid · Accepted Answer

(i) We know sin 45° = (1/√2) and cos 45° = (1/√2) (From the table)

⇒

(ii) We know sin 30° = 1/2 and tan 45° = 1 (From the table)

⇒

(iii) We know tan 30° = (1/√3) (From the table)

tan 45° = 1

tan 60° = √3

⇒

(iv) We know sin 30° = cos 60° = 1/2 (From the table)

tan 30° = cot 60° = 1/√3

⇒

(v) We know that cos 90° = 0 , sin 90° = 1 and tan 45° = 1 (From the table)

⇒ 6(0)² + 3(1)² + 4(1)²

⇒ 3 + 4

⇒ 7

(vi) We know cot 60° = (1/√3) (From the table)

sec 30° = 2/√3

sin 45° = 1/√2

sin 60° = √3/2

cos 45° = 1/√2

⇒

(vii) We know tan 60° = √3 (From the table)

cos 45° = 1/√2

sec 30° = 2/√3

cos 90° = 0

cosec 30° = 2

sec 60° = 2

cot 30° = √3

⇒

⇒ 9

(viii) We know

sin 30° = cos 60° = 1/2 (From the table)

cos 45° = 1/√2

sin 90° = 1

⇒ 4(

⇒ 2

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°)

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