Question

It sinx = cosx then find the value
of 2tan x + cos2x​

Answer 1

Correct question :-

If sin x = cos x then find the value of 2tan x + cos² x and 2tan x + cos 2x

sin x = cos x

This is possible only when x = 45° as sin 45° = cos 45° = 1/√2

⇒ x = 45°

Now, 2tan x + cos² x

= 2tan 45° + cos² 45

= 2(1) + cos² 45°

[ Because tan 45° = 1 ]

= 2 + (1/√2)²

[ Because cos90° = 0 ]

= 2 + 1/2

= (4 + 1)/2

= 5/2

Now, 2tan x +cos 2x

= 2tan 45° + cos 2(45°)

= 2(1) + cos 90°

= 2 + 0

= 2

Hence, the value 2tan x + cos² x is 5/2 and the value of 2tan x + cos 2x is 2.

Answer 2

Correct Question :------

• if sinx = cosx and x is an acute angle , Find the value of 2tanx + cos2x ..... ?

Solution :-----------

it is given that,,,

sinx = cosx

Dividing both sides by cosx we get,,,

→ sinx/cosx = cosx/cosx

→ Tanx = 1 [ since sin@/cos@ = tan@]

→ x = tan^(-1)1

→ x = 45° or 225° ...

But it is given that, x is an acute angle ,

Hence, x = 45°...

___________________

Now,

→ 2tanx + cos2x

→ 2tan45° + cos2(45°)

→ 2tan45° + cos90° .

Now, we know that,,,

Tan45° = 1

cos90° = 0

Putting values ,

→ 2×1 + 0

→ 2 (Ans) ...

Hence, our required answer will be 2...

(Hope it Helps you)