Question

prove that: (class XI trigonometry)

(sum no. ii)

Answer 1

here I am writing theta as A, because it is difficult for me to write theta always.

$\frac{sinA-cosA + 1}{sinA+cosA-1} * \frac{sinA+cosA+1}{sinA+cosA+1}$

$\frac{sin^2A + sinAcosA + sinA - sinAcosA- cos^2A - cosA+sinA + cosA+1}{(sinA+cosA)^2 - 1}$

$\frac{sin^2A + sinA - cos^2A + sinA + 1}{(sinA + cosA)^2 - (1)^2}$

We know that 1 - cos^2A = sin^2A

$\frac{sin^2A + sin^2A + sinA + sinA}{sin^2A + cos^2A + 2sinAcosA - 1}$

$\frac{2sin^2A+2sinA}{sin^2A+cos^2A+2sinAcosA-1}$

$\frac{2sin^2A + 2sinA}{1 + 2sinAcosA - 1}$

$\frac{2sin^2A + 2sinA}{2sinAcosA}$

$\frac{2sinA(1+sinA)}{2sinAcosA}$

$\frac{1+sinA}{cosA}$


LHS = RHS.


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks