Question

If sinx.cosx=k,thensinx+cosx=?

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\boxed{sin(x) + cos(x) = ±\sqrt{1 + 2k}}$

⍟ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ⍟

Now,

$\:\:\:\: [sin(x) + cos(x)]^2$

$= sin^2(x) + cos^2(x) + 2sin(x)cos(x)$

$= 1 + 2sin(x)cos(x)$

$= 1 + 2k$

$\implies sin(x) + cos(x) = ±\sqrt{1 + 2k}$