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Express each of the following in terms ...

Express each of the following in terms of trigonometric ratios of angles between `0^(@)and 45^(@)`
(i) `sin70^(@)+sec70^(@)` " " (ii) `tan65^(@)+"cosec "65^(@)` " " (iii) ``cos81^(@)+cot80^(@)`

Text Solution

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(i) `sin70^(@)+sec70^(@)=sin(90^(@)-20^(@))+sec(90^(@)-20^(@))=cos20^(@)+"cosec " 20^(@)`
(ii) `tan65^(@)+"cosec " 65^(@)=tan(90^(@)-25^(@))+"cosec"(90^(@)-25^(@))=cot25^(@)+sec25^(@)`
(iii) `cos81^(@)+cot80^(@)=cos(90^(@)=9^(@))+cot(90^(@)-10^(@))=sin9^(@)+tan10^(@)`
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