Question

Tan 80° × tan10^0++ sin^2 70° + sin ^2 20°is ​

Answer 1

Answer:

tan80×tan10+sin

2

70+sin

2

20

Now, tan80

∘

=cot(90−80)

∘

=cot10

∘

....(1)

Also, sin70

∘

=cos(90−70)

∘

=cos20

∘

.....(2)

From (1) and (2)

=cot10

∘

×tan10

∘

+cos

2

20

∘

+sin

2

20

=1+1=2.

Answer 2

Answer:

tan 80° × tan 10° + sin² 70° + sin² 20° = 2//

Step-by-step explanation:

tan 80° × tan 10° + sin² 70° + sin² 20°

= tan (90°-10°) × tan 10° + sin² (90° - 20°) + sin² 20°

= cot 10° × tan 10° + cos² 20° + sin² 20°

= 1/tan 10° × tan 10° + 1

= 1 + 1

= 2//

Rules used:

Complimentary angle rules: tan (90-θ) = cot θ and sin²(90-θ) = cos² θ

Trigonometric identities: sin²θ + cos²θ = 1

cot θ = 1/tanθ

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