Question

show that
if sec+tan=m​

Answer 1

Answer:

See i m not writing theta, or else it will be too much to type

Step-by-step explanation:

sec + tan = m

To prove,

m²-1/(m²+1) = sin

m²= sec²+2sectan+tan²

Now, sec²= 1+tan²

Replace it over here,

1+ 2tan² + 2sectan

m²-1= 2tan²+2sectan

m²+1 is 2+ 2tan²+ 2sectan

2 is a common factor, on division it gets cancelled out.

Now, we have

tan(sec+tan)/sec(sec+ tan)

I can write this because 1+tan²= sec²

Cancel out sec+tan

We have tan/sec or (sin/cos)/(1/cos)

cos goes up, we are it gets cancelled out, we are left with sin.

Hence proved