Question

Sin-cos
finda Tan²+sin2 -1​

Answer 1

Answer:

Step-by-step explanation:

2-cos^2 x=3sin x cos x

1+1-cos^2 x=3sin x cos x

1+sin^2 x=3 sin x cos x

1+sin^2 x+cos^2 x=3sinx cos x+cos^2 x ( adding cos^2 x both sides)

2=cos x(3 sin x +cos x)

2/cos x=3 sin x+cos x

2 sec x=3 sin x+ cos x

2 sec^2 x=3 sin x sec x+ cos x sec x

2 sec^2 x= 3sin x/cos x+1

2 sec^2 x=3 tan x+ sec^2 x-tan^2 x

( By writing 1=sec^2 x-tan^2 x)

Sec^2 x+tan^2 x=3tan x

sec^2 x-tan^2 x=3 tan x-2tan^2 x

1=3 tan x-2 tan^2 x

2 tan^2 x-3 tan x+1=0

By solving it we are getting two values of tan x that are 1/2 and 1

But the value of 1 will be rejected because tan^-1 (1)=45° and for 45° both sin x = tan x and it is provided in the question that the value of sin x is not equal to cos x hence the value of tan x =1/2=0.5