Math, asked by dudonjennerdj, 5 days ago

Please solve these questions

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Answered by Anonymous
1

3. sec 4A = cosec (A-20)

→ 1/cos 4A = 1/sin (A-20)

→ sin (A-20) = cos 4A

→ sin (A-20) = sin (90-4A) [cos x = sin (90-x)]

→ A - 20 = 90 - 4A

→ 5A = 110

→ A = 22°

4. To prove- cotA + tanA = secA . cosecA

L.H.S.- cotA + tanA = 1/tanA + tanA

→ 1+tan²A/tanA

→ sec²A/tanA

→ sec²A/sinA.secA

→ secA/sinA = secA . cosecA = R.H.S

HENCE PROVED

5. a cosx - b sinx = x

a sinx + b cosx = y

x²+y² = a²cos²x + b²sin²x - 2abcosxsinx + a²sin²x + b²cos²x + 2absinxcosx

→ x²+y² = a²(cos²x + sin²x) + b²(cos²x + sin²x)

→ x²+y² = a²+b² [cos²x+sin²x=1]

6. L.H.S.- (1 + tan²x) + (1 + 1/tan²x)

→ (sec²x) + (1 + cot²x) [1+tan²x=sec²x]

→ sec²x + cosec²x [1+cot²x=cosec²x]

→ 1/cos²x + 1/sin²x

→ sin²x+cos²x/sin²x cos²x

→ 1/sin²x(1-sin²x)

→ 1/sin²x - sin⁴x

HENCE PROVED

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