sin-x-3cos-x-tan-x-3-True-or-false-

Question Number 12905 by 433 last updated on 06/May/17

\sin (x) = 3 \cos (x) \Leftrightarrow \tan (x) = 3

T r u e o r f a l s e ?

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17

1) f a l s e i f : c o s x = 0 \Rightarrow x = 2 k π + \frac{π}{2}

2) t r u e i f x \neq 2 k π + \frac{π}{2}, k \in Z .

Commented by mrW1 last updated on 07/May/17

i f \cos x = 0, t h e n \sin x = \pm 1 \neq 3 \times 0

\Rightarrow \cos x \neq 0

t h e r e f o r e :

\sin x = 3 \cos x

\Leftrightarrow \tan x = 3

Answered by mrW1 last updated on 07/May/17

t r u e!

Commented by prakash jain last updated on 07/May/17

a)

\sin x = 3 \cos x \Rightarrow \frac{\sin x}{\cos x} = 3 \Rightarrow \tan x = 3

b)

\tan x = 3 \Rightarrow \frac{\sin x}{\cos x} = 3 \Rightarrow \sin x = 3 \cos x

h e n c e

\sin x = 3 \cos x \Leftrightarrow \tan x = 3

Commented by prakash jain last updated on 07/May/17

question requires \Leftrightarrow so both

needs to be shown .