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Without using trigonometric tables, eval...

Without using trigonometric tables, evaluate :
(i) `cos 48^@-sin42^@`
(ii) `cosec31^@-sec59^@`
(iii) `cot 34^@-tan56^@`
(iv)` cos^2 13^@-sin^2 77^@`

Text Solution

Verified by Experts

We have
(i) `cos 48^@-sin42^@ =cos (90^@-42^@)-sin 42^@=sin 42^@-sin 42^@=0 [because cos (90^@-theta)=sin theta]`.
(ii) ` cosec 31^@-sec 59^@=cosec(90^@-59^@)-sec 59^@=sec59-sec59^@=sec 59^@-sec 59^@=0 [because cosec (90^@-theta)=sec theta]`.
(iii) `cot34^@-tan56^@=cot (90^@-56^@)-tan 56^@=tan 56^@-tan 56^@=0 [because cot (90^@-theta)tan theta]`.
(iv)` cos^2 13^@-sin^2 77 =cos^2(90^@-77^@)-sin^2 77^@=sin^2 77^@-sin ^2 77^@=0 [because cos (90^@-theta)=sin theta]`.
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