Question

Express each of the following in terms of T-ratios of angles lying between $0^{\circ }and{45}^{\circ }:$

(i) $sin{67}^{\circ }+cos{75}^{\circ }$ (ii) $cot{65}^{\circ }+tan{49}^{\circ }$

(iii) $sec{78}^{\circ }+cosec{56}^{\circ }$ (iv) $cosec{54}^{\circ }+sin{72}^{\circ }$

Answer 1

(i) $sin{67}^{\circ }+cos{75}^{\circ }$

$=cos({90}^o–{67}^o)+sin({90}^o–{75}^o)$

$=cos{23}^o+sin{15}^o$

(ii) $cot{65}^{\circ }+tan{49}^{\circ }$

$=tan({90}^o–{65}^o)+cot({90}^o–{49}^o)$

$=tan{25}^o+cot{41}^o$

(iii) $sec{78}^{\circ }+cosec{56}^{\circ }$

$=sec({90}^o–{12}^o)+cosec({90}^o–{34}^o)$

$=cosec{12}^o+sec{34}^o$

(iv) $cosec{54}^{\circ }+sin{72}^{\circ }$

$=sec({90}^o–{54}^o)+cos({90}^o–{72}^o)$

$=sec{36}^o+cos{18}^o$