Question

if 6cosa - sina= 4
then find 6cosa + sina.​

Answer 1

Answer:

- 4

Step-by-step explanation:

the answer of your question is -4

Answer 2

The value of $6\sin A +\cos A$ =  ± $\sqrt{21}$

Step-by-step explanation:

Given,

$6\cos A -\sin A= 4$              ........ (1)

Let $6\sin A +\cos A= x$        ........ (2)

To find, the value of $6\sin A +\cos A$ = ?

Squaring and adding equations (1) and (2), we get

$(6\cos A -\sin A)^2+(6\sin A +\cos A)^2= 4^2+x^2$

⇒ $36\cos^2 A +\sin^2 - 12\cos A\sin A+36\sin^2 A +\cos^2A+12\cos A\sin A= 4^2+x^2$

⇒ $36\cos^2 A +\sin^2+36\sin^2 A +\cos^2A= 4^2+x^2$

⇒ $36(\cos^2 A +\sin^2A)+(\sin^2 A +\cos^2A)=16+x^2$

⇒ $36(1)+1=16+x^2$

Using the trigonometric identity,

$\cos^2 A +\sin^2A = 1$

⇒ 36 + 1 = 16 + $x^2$

⇒ 37 = 16 + $x^2$

⇒ $x^2$ = 37 - 16 = 21

∴ x = ± $\sqrt{21}$

Thus, the value of $6\sin A +\cos A$ =  ± $\sqrt{21}$