Question

If 2sin theta=sec theta, then the value of sin^4 theta+cos^4 theta

Answer 1

$--> 2 \sin\alpha = \sec \alpha \\ \therefore 2 \sin\alpha = \frac{1}{ \cos\alpha } \\ \therefore \: 2\sin\alpha \cos\alpha = 1 \\ \therefore \: \sin2 \alpha = 1 \\ \therefore \: 2 \alpha = \frac{\pi}{2} \\ \therefore \: \alpha = \frac{\pi}{4} \: \: \: \\ \\ now \: \\ \\ \sin^{4} \alpha + \cos^{4} \alpha \\ \\ = { \sin }^{4} \frac{\pi}{4} + { \cos }^{4} \frac{\pi}{4} \\ \\ = { (\frac{1}{ \sqrt{2} }) }^{4} + ( { \frac{1}{ \sqrt{2} } )}^{4} \\ \\ = \frac{1}{4} + \frac{1}{4} \\ \\ = \frac{1}{2}$
hope this helps..........