If tan7θ.tan2θ = 1, then the value of tan3θ is?
A. $$\sqrt 3 $$
B. $$ - \frac{1}{{\sqrt 3 }}$$
C. $$\frac{1}{{\sqrt 3 }}$$
D. $$ - \sqrt 3 $$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \tan 7\theta .\tan 2\theta = 1 \cr & \left[ {{\text{If tan A}}{\text{.tan B}} = {\text{1}}} \right] \cr & ({\text{then, A}} + {\text{B}} = {90^ \circ }) \cr & \left( {7\theta + 2\theta } \right) = {90^ \circ } \cr & 9\theta = {90^ \circ } \cr & \theta = {10^ \circ } \cr & \Rightarrow \tan 3\theta \cr & \Rightarrow \tan {30^ \circ } \cr & \Rightarrow \frac{1}{{\sqrt 3 }} \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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