Question

Prove the following:

(i) $sin\theta sin({90}^o-\theta )-cos\theta cos({90}^o-\theta )=0$
(ii) $\frac{cos({90}^o-\theta )sec({90}^o-\theta )tan\theta }{cosec\left({90}^o\right)sin({90}^o-\theta )cot({90}^o-\theta )}+\frac{tan({90}^o-\theta )}{cot\theta }=2$
(iii) $\frac{tan({90}^o-A)cotA}{cose{c}^{2}A}-co{s}^{2}A=0$
(iv) $\frac{cos({90}^o-A)sin({90}^o-A)}{tan({90}^o-A)}=si{n}^{2}A$
(v) $sin({50}^o+\theta )-cos({40}^o-\theta )+tan{1}^{o}tan{10}^{o}tan{20}^{o}tan{70}^{o}tan{80}^{o}tan{89}^o=1$

Answer 1