Evalute the following:

(i) $$\dfrac{sin 20°}{ cos 70°}$$

(ii) $$\dfrac{ cos 19°}{ sin 71°}$$

(iii) $$\dfrac{sin 21°}{ cos 69°}$$

(iv) $$\dfrac{tan 10°}{ cot 80°}$$

(v) $$\dfrac{sec 11°}{ cosec 79°}$$

Asked by Aaryan | 9 months ago |  188

##### Solution :-

(i) We have,

= $$\dfrac{sin (90° – 70°)}{ cos 70°} =\dfrac{ cos 70°}{cos70° }=1$$ [∵ sin (90 – θ) = cos θ]

(ii) We have,

= $$\dfrac{ cos (90° – 71°)}{ sin 71°} = \dfrac{sin 71°}{ sin 71°}$$ = 1 [∵ cos (90 – θ) = sin θ]

(iii) We have,

$$\dfrac{sin 21°}{ cos 69°} = \dfrac{sin (90° – 69°)}{ cos 69°} = \dfrac{cos 69°}{ cos69°}$$ = 1 [∵ sin (90 – θ) = cos θ]

(iv) We have,

$$= \dfrac{tan (90° – 10°) }{ cot 80° }= \dfrac{cot 80°}{ cos80°}$$ = 1 [∵ tan (90 – θ) = cot θ]

(v) We have,

=$$\dfrac{ sec (90° – 79°)}{ cosec 79°} = \dfrac{cosec 79°}{ cosec 79°}$$ = 1

[∵ sec (90 – θ) = cosec θ]

Answered by Aaryan | 9 months ago

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