Question

If 8cos x + 15sin x = 15and cos x = 0 then 8sin x - 15cos x =​

Answer 1

8 cosx+15sinx=15 --------- (1)

and cosx≠0, then 8 sinx−15cosx=?

squaring and adding both the equations, we get,

$\small \bold{(8cosx+15sinx)^2+(8sinx−15cosx)^2}$

$\small \bold{64(cos^2 x+sin^2 x)+225(cos^2 x+sin^2 x)=289}$

$\small \bold{(8sinx−15cosx)^2=289−15^2 =64}$

∴8sinx−15cosx=±8

∴8sinx−15cosx=8 ----------(2)

∴8sinx−15cosx=−8 --------(3)

Adding (1) and (2)

∴23sinx−7cosx=23 This relation is possible only if cosx=0 but given condition is cosx≠0

So relation (2) is rejected and relation (3) is accepted.