Trigonometric Functions — MATHS STD 11 Science — Question

4. 194

Solution:

We have:

$\tan\text{A}+\cot\text{A}=4$

squaring both the sides:

$(\tan\text{A}+\cot\text{A})^2=4^2$

$\Rightarrow\tan^2\text{A}+\cot^2\text{A}+2(\tan\text{A})(\cot\text{A})=16$

$\Rightarrow\tan^2\text{A}+\cot^2\text{A}+2=16$

$\Rightarrow\tan^2\text{A}+\cot\text{A}=14$

squaring both the sides again:

$(\tan^2\text{A}+\cot^2\text{A})^2=14^2$

$\tan^4\text{A}+\cot^4\text{A}+2(\tan^2\text{A})(\cot^2\text{A})=196$

$\Rightarrow\tan^4\text{A}+\cot^4\text{A}+2=196$

$\Rightarrow\tan^4\text{A}+\cot^4\text{A}=194$