Question

The least value of 2sin square thita + 3cos square thita is​

Answer 1

Your Answer:

We have to find the least value of ${\tt 2\sin^{2}\theta+3\cos^{2}\theta}$

Solving

$\tt {\tt 2\sin^{2}\theta+3\cos^{2}\theta}\\\\=2\sin^{2}\theta+2\cos^{2}\theta+\cos^{2}\theta\\\\=2(\sin^{2}\theta+\cos^{2}\theta)+\cos^{2}\theta\\\\=2(1)+\cos^{2}\theta\\\\=2+\cos^{2}\theta\\\\The\:minimum\:value\:of \:\cos^{2}\theta=0,\: \\\\So,\:putting\: value \:of\: \cos^{2}\theta\\\\=2+0\\\\=2$

The minimum value of this is 2.

Answer 2

your answer refer to the attachment.....

• Explanation

• using identity $sin\theta+cos\theta=1$

• we know $cos^2\theta=0$