Question

Sinx=cosx then 2tanx+cos^2x

Answer 1

it is given that , sinx = cosx

we know, at x = π/4 , sinx = cosx = 1/√2

so, x = π/4 or 45°

now, 2tanx + cos²x

= 2tanπ/4 + cos²π/4

= 2 × 1 + (1/√2)²

= 2 + 1/2

= 5/2

hence, answer is 5/2

Answer 2

Answer:

1 + cos²x

Step-by-step explanation:

given sin x = cos x

to find 2 tanx + cos²x               ...............(i)

we know that by trignometric rules

tan x = $\frac{sin x}{cos x}$

puti in (i)

2 tanx + cos²x  = $\frac{sin x}{cos x}$ + cos²x

is sinx = cos x

put value

2 tanx + cos²x  = $\frac{sin x}{sin x}$ + cos²x

2 tanx + cos²x  = 1 + cos²x