Question

x sin²30° cos²60°/4 cos² 45° = 3 sin²45° + 2 cos²30°/sin²90° - 4 cos²45° .Find the value of x.​

Answer 1

Question :- (x*sin²30°*cos²60°)/(4*cos² 45°) = (3*sin²45° + 2 cos²30°)/(sin²90° - 4*cos²45°) . Find the value of x. ?

Solution :-

we know that,

• sin 30° = (1/2)
• cos 60° = (1/2)
• cos 45° = (1/√2)
• sin 45° = (1/√2)
• cos 30° = (√3/2)
• sin 90° = 1

Solving LHS part now :-

→ (x*sin²30°*cos²60°)/(4*cos² 45°)

→ [x * (1/2)² * (1/2)²] / [4 * (1/√2)²]

→ [x * (1/4) * (1/4)] / [ 4 * (1/2) ]

→ (x/16) / 2

→ (x/16) * (1/2)

→ (x/32)

Solving RHS part now :-

→ (3*sin²45° + 2 cos²30°)/(sin²90° - 4*cos²45°)

→ [ 3 * (1/√2)² + 2 * (√3/2)² ] / [(1)² - 4 * (1/√2)²]

→ [ 3 * (1/2) + 2 * (3/4) ] / [ 1 - 4 * (1/2) ]

→ [ (3/2) + (3/2) ] / [ 1 - 2 ]

→ (6/2) / (-1)

→ 3 * (-1)

→ (-3)

therefore,

→ LHS = RHS

→ (x/32) = (-3)

→ x = (-96) (Ans.)

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