Question

tana+cota=2 then find the value of tan^3a+7cot^3a

Answer 1

Answer:

6

Step-by-step explanation:

Hi

let x = tan a

y = cot a

Given tana + cota = 2

x + y = 2

xy = tana*cota = 1

Consider (x + y)³ = x³ + y³ + 3xy(x + y)

But we know that xy = 1 and x + y = 2, so

2³ =  x³ + y³ + 3(2)

On simplifying the constants and rearranging the terms, we get

x³ + y³ = 8 - 6

= 2

tan³a + cot³a = 6

Hope, it helps !

Answer 2

Answer:

Ans is 8

Step-by-step explanation:

Take the given equation

$\frac{sina}{cosa}+\frac{cosa}{sina}=2\\\ \\ \frac{sin^2a+cos^2a}{sina\cdot cosa}=2\\ \\ 1=2Sina.cosa \\ \\ 1=sin\left(2a\right) \\ \\ 2a=\frac{\pi }{2}+2\pi n \\\\a=\frac{\pi }{4}+\pi n$

Hence now we substitute value of a =$\frac{\pi }{4}$

in the equation $tan^3a+7cot^3a$

we get 1+7=8

If you need to solve it fast you need to just let a value of a that is pi/4 which satisfy the given condition and then substitute the value of a in the  

tan^3a+7cot^3a you will get 8 because $tan\left(\frac{\pi }{4}\right)=cot\left(\frac{\pi }{4}\right)=1$