Question

sin theta + cos theta = a
then
sin power 4 theta + cos power 4 theta = ​

Answer 1

Step-by-step explanation:

i have sent the answer above

Answer 2

Answer:

The value of (sin⁴θ + cos⁴θ) is $1-2[\frac{(1-a)^{2}}{2}]^{2}$.

Step-by-step explanation:

It is provide that: sin θ + cos θ = a.

Then

$(sin\theta+cos\theta)^{2}=sin^{2}\theta+cos^{2}\theta+2sin\theta\ cos\theta\\a^{2}=1+2sin\theta\ cos\theta\\2sin\theta\ cos\theta=1-a^{2}\\sin\theta\ cos\theta=\frac{(1-a)^{2}}{2}$

Solve for sin⁴θ + cos⁴θ as follows:

$(sin^{2}\theta+cos^{2}\theta)^{2}=sin^{4}\theta+cos^{4}\theta+2sin^{2}\theta\ cos^{2}\theta\\1=sin^{4}\theta+cos^{4}\theta+2(sin\theta\ cos\theta)^{2}\\1=sin^{4}\theta+cos^{4}\theta+2[\frac{(1-a)^{2}}{2}]^{2}\\sin^{4}\theta+cos^{4}\theta=1-2[\frac{(1-a)^{2}}{2}]^{2}$

Thus, the value of (sin⁴θ + cos⁴θ) is $1-2[\frac{(1-a)^{2}}{2}]^{2}$.