Question

(cosec-cos)^2 = 1-cos/1+cos Prove it

Answer 1

Answer:

Step-by-step explanation:

i have attached a file. pls refer to it

Answer 2

We can prove it in different way,

by solving RHS.

★[If you want any other method, then check my another answer:

https://brainly.in/question/18394752]

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Using Identity:

• 1 - cos²Θ = sin²Θ
• 1/sinΘ = cosecΘ
• cosΘ/sinΘ = cotΘ

Answer:

$\tt \implies RHS = \dfrac{1 - cos \theta}{1 + cos \theta} \\ \\ \tt \implies RHS = \dfrac{1 - cos \theta}{1 + cos \theta} \times \dfrac{1 - cos \theta}{1 - cos \theta} ....(rationalisation) \\ \\ \tt \implies RHS = \dfrac{1 -cos {}^{2} \theta }{sin {}^{2} \theta} \\ \\ \tt \implies RHS = ( \dfrac{1 - cos \theta}{sin \theta} ) {}^{2} ....(square \: common)\\ \\ \tt \implies RHS = ( \frac{1}{sin \theta} - \dfrac{cos \theta}{sin \theta} ) {}^{2} \\ \\ \tt \implies RHS = (cosec \theta - cot \theta) {}^{2}$

$\large \implies \boxed {\boxed {\tt \blue {RHS = LHS }}}$

$\\ \large\bold\red{\: \: \: \: \: \: \: \: \: \: Hence \: \: Proved}$