when-sinx-cosx-1-4-find-sinx-cosx-

Question Number 189916 by mustafazaheen last updated on 24/Mar/23

when sinx \times cosx = - \frac{1}{4}

find sinx + cosx = ?

Answered by aminitindas last updated on 24/Mar/23

Ans :

{(\sin x + \cos x)}^{2} = \sin^{2} x + \cos^{2} x + 2 \sin x \cos x

{(\sin x + \cos x)}^{2} = 1 + 2 (- \frac{1}{4}) = 1 - \frac{1}{2} = \frac{1}{2}

\sin x + \cos x = \pm \frac{1}{\sqrt{2}}

a m i n i t i n d a s, March 24,^{'} 23

Answered by CElcedricjunior last updated on 26/Mar/23

{\begin{cases} s i n x \times c o s x = - \frac{1}{4} \\ s i n x + c o s x = k \end{cases}

c a l c u l o n s s i n x + c o s x = k M o i v r e

o n {(c o s x + s i n x)}^{2} = 1 + 2 s i n x c o s x

= \frac{1}{2}

s i n x + c o s x = \mp \frac{\sqrt{2}}{2}

L e m i g n o n f o f a n a c e d r i c j u n i o r