If $${\text{se}}{{\text{c}}^2}\theta + {\text{ta}}{{\text{n}}^2}\theta = \frac{7}{{12}}{\text{,}}$$ then $${\text{se}}{{\text{c}}^4}\theta $$ - $${\text{ta}}{{\text{n}}^4}\theta $$ = ?
A. $$\frac{7}{{12}}$$
B. $$\frac{1}{2}$$
C. $$\frac{7}{2}$$
D. 1
Answer: Option A
Solution (By Examveda Team)
$$\eqalign{ & \left( {{\text{se}}{{\text{c}}^4}\theta - {\text{ta}}{{\text{n}}^4}\theta } \right) \cr & \Rightarrow \left( {{\text{se}}{{\text{c}}^2}\theta - {\text{ta}}{{\text{n}}^2}\theta } \right)\left( {{\text{se}}{{\text{c}}^2}\theta + {\text{ta}}{{\text{n}}^2}\theta } \right) \cr & \Rightarrow 1 \times \left( {{\text{se}}{{\text{c}}^2}\theta + {\text{ta}}{{\text{n}}^2}\theta } \right)[1 + {\text{ta}}{{\text{n}}^2}\theta = {\text{se}}{{\text{c}}^2}\theta ] \cr & \Rightarrow 1 \times \frac{7}{{12}} \cr & \Rightarrow \frac{7}{{12}} \cr} $$This Question Belongs to Arithmetic Ability >> Trigonometry
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