Question

tan
1+tanx
IT
+ X
4
-tang
7
tan
х
4​

Answer 1

Answer: =tan(π4+x2)=RHS

Text Solution

Solution

We have

LHS=cosx(1−sinx)

=(cos2.x2−sin2.x2)(cos2.x2+sin2.x2−2sin.x2cos.x2)

⎡⎣⎢⎢∵cosx=(cos2.x2−sin2.x2),cos2.x2+sin2.x2=1 and sinx=2sin.x2cos.x2⎤⎦⎥⎥

=(cos.x2+sin.x2)(cos.x2+sin.x2)(cos.x2−sin.x2)

=(cos.x2+sin.x2)(cos.x2−sin.x2)=(1+tan.x2)(1−tan.x2)=(tan.π4+tan.π2)(1−tan.π4.tan.x2)

[dividing num. and denom . by cos .x2]

=tan(π4+x2)=RHS

Step-by-step explanation: