Question

Expresss each of the following in terms of T-ratios of angles lying between `0^theta and 45^@`.
(i) `sin 67^@+cos 75^@`
(ii) ` cot 65^@+tan 49^@`
(iii) ` sec 78^@+cosec 56^@`
(iv) `cosec 54^@+sin 72^@`.

Answer 1

Correct Answer - `(i) cos 23^@+sin 15^@`
`(ii) tan 25^@+cot 41^@`
`(iii) cosec 12^@+sec34^@`
`(iv) sec 36^@+cos 18^@`
`(i) sin 67^@+cos 75^@=sin (90^@-23^@)+cos (90^@-15^@)=cos23^@+sin 15^@`.
`(ii) cot 65^@+tan 49^@=cot (90^@-25^@)+tan (90^@-41^@)=tan 25^@+cot 41^@`.