Question

if cosec^2 - tetha (1+ cos tetha) (1- cos tetha) = x ,then find the value of x​

Answer 1

CORRECT QUESTION :-

★ If cosec²ϴ (1 + cos ϴ)(1 - cos ϴ) = x, Then find the value of x.

GIVEN :-

• cosec²ϴ (1 + cos ϴ)(1 - cos ϴ) = x

TO FIND :-

• The value of x.

SOLUTION :-

→ cosec²ϴ (1 + cos ϴ)(1 - cos ϴ) = x

→ x = cosec²ϴ (1 + cos ϴ)(1 - cos ϴ)

• [ Using identity :- (a + b)(a - b) = a² - b² ]

→ x = cosec²ϴ[(1)² - (cos ϴ)²]

→ x = cosec²ϴ (1 - cos²ϴ)

• [ Using identity :- 1 - cos²ϴ = sin²ϴ ]

→ x = cosec²ϴ × sin²ϴ

• [ By using identity :- sin²ϴ = (1/cosec²ϴ) ]

→ x = cosec²ϴ × 1/cosec²ϴ

→ x = 1

★ Hence the value of x is 1.

Answer 2

$\huge\bf\red{Solution}$

Given

cosec²∅ (1 + cos∅) (1 + cos∅) = x

To Find

Now, we have to find out the value of x in this given equation.

Solve

=> cosec²∅ (1 + cos∅) (1 + cos∅) = x

=> x = cosec²∅ (1 + cos∅) (1 + cos∅)

As we have studied the formula of (a² - b²) in polynomial chapter.

★ (a² - b²) = (a + b) (a - b) ★

By the help of this formula, we can solve this question.

=> x = [cosec²∅ {(1)² - (cos∅)²}]

=> x = cosec²∅ (1 - cos²∅)

As we know that,

★ 1 - cos²∅ = sin²∅ ★

=> x = cosec²∅ × sin²∅

As we know that,

★ 1/cosec²∅= sin²∅ ★

=> x = cosec²∅ × 1/cosec²∅

[[ .°. x = 1 ]] ← Answer

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