Question

Evaluate the following :

(i) ${\left(\frac{\sin 49°}{\cos 41°}\right)}^2+{\left(\frac{\cos 41°}{\sin 49°}\right)}^2$
(ii) cos 48° − sin 42°
(iii) $\frac{\cot 40°}{\tan 50°}-\frac{1}{2}\left(\frac{\cos 35°}{\sin 55°}\right)$
(iv) ${\left(\frac{\sin 27°}{\cos 63°}\right)}^2-{\left(\frac{\cos 63°}{\sin 27°}\right)}^2$
(v) $\frac{\tan 35°}{\cot 55°}+\frac{\cot 78°}{\tan 12°}-1$
(vi) $\frac{\sec 70°}{\mathrm{cosec}20°}+\frac{\sin 59°}{\cos 31°}$
(vii) cosec 31° − sec 59°
(viii) (sin 72° + cos 18°) (sin 72° − cos 18°)
(ix) sin 35° sin 55° − cos 35° cos 55°
(x) tan 48° tan 23° tan 42° tan 67°
(xi) sec50° sin 40° + cos40° cosec 50°

Answer 1

(i) We have to find:

Since and

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So value of is

(ii) We have to find:

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So value of is

(iii) We have to find:

Since and

So value of is

(iv) We have to find:

Since and

So value of is

(v) We have to find:

Since and

So value of is

(vi) We have to find:

Sinceand

So

So value of is

(vii) We have to find:

Since.So

So value of is

(viii) We have to find:

Since.So

So value of is

(ix) We find:

Sinceand

So value of is

(x) We have to find

Since.So

So value of is

(xi) We find to find

Since, and .So

So value of is