Question

Find the value of 4 tan 4A + 8 cot 8A

• A. 4tan4A
• B. 4cot4A
• C.
• D.

Answer 1

Answer: (B), (D)

The correct options are
B

4cot4A

D

To perform operations on these two terms.We should bring both the terms on same angle.So, 8A can be written as 2 $\times$ 4A

So, 4tan4A + $\frac{8}{tan8A}$

= 4tan4A + $\frac{8}{tan2\left(4A\right)}$

= 4tan4A + $\frac{8}{\frac{2tan4A}{(1-ta{n}^{2}4A)}}$

= 4tan4A + $\frac{4(1-ta{n}^{2}4A)}{tan4A}$

= $\frac{4ta{n}^{2}4A+4-4ta{n}^{2}4A}{tan4A}$

= $\frac{4}{tan4A}$ = 4cot4A(Option B)

= $\frac{\frac{4}{2ta{n}^{2}A}}{(1-ta{n}^{2}2A)}$ = $\frac{2(1-ta{n}^{2}2A)}{tan2A}$ (Option D)