Question

Prove 1+cos teeta/ sin teeta - sin teeta /1+cos teeta = 2cos teeta

Answer 1

Answer:

1+COS TEETA/SIN TEETA-SIN TEETA/1+COS TEETA=2 COS TEETA

APROOF:-

Step-by-step explanation:

*1+COS.square+2 cos TEETA-SIN.squareteeta/1+Costeeta×sinteeta

*2cos.squareteeta+2 costeeta/(1+costeeta)(sinteeta)

*2costeeta(1+costeeta)/(1+costeeta)(sinteeta)

=2cotteeta

Answer 2

Answer:

$\red { \frac{1+cos\theta}{sin\theta} - \frac{sin\theta}{1+cos\theta}} \green {=2cot\theta}$

Step-by-step explanation:

$LHS = \frac{1+cos\theta}{sin\theta} - \frac{sin\theta}{1+cos\theta}\\= \frac{ (1+cos\theta)^{2} - sin^{2}\theta }{sin\theta (1+cos\theta) }$

$= \frac{ 1+ cos^{2}\theta+ 2cos\theta - sin^{2}\theta }{sin\theta (1+cos\theta) }$

$= \frac{ cos^{2}\theta+ 2cos\theta +( 1 - sin^{2}\theta )}{sin\theta (1+cos\theta) }$

$= \frac{ cos^{2}\theta + 2cos\theta + cos^{2}\theta }{sin\theta(1+cos\theta)}$

$= \frac{ 2cos^{2}\theta + 2cos\theta }{sin\theta(1+cos\theta)}$

$= \frac{ 2cos\theta( cos\theta+1)}{sin\theta(cos\theta+1)}\\= 2\frac{cos\theta}{sin\theta}\\= 2cot\theta\\= RHS$

Therefore.,

$\red { \frac{1+cos\theta}{sin\theta} - \frac{sin\theta}{1+cos\theta}} \green {=2cot\theta}$

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