Question

if tan a + cot a is equals to 4 then find Tan 5A + cot 5A​

Answer 1

Answer:

tanA+cotA=4

(squaring both sides)

(tanA+cotA)2=42

⇒tan2A+cot2A+2(tanA)(cotA)=16

⇒tan2A+cot2A+2=16

⇒tan2A+cot2A=16−2

⇒tan2A+cot2A=14

(on squaring both sides)

⇒(tan2A−cot2A)2=(14)2

tan4A+cot4A+2(tan2A)(cot2A)=196

tan2A+cot4A=196−2

=194

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Answer 2

hope this ans will help you

Answer:

If tanA+cotA=4, then what is the value of tan^6A+cot^6A?

Let tanA=a and cotA=b

Therefore, a+b = 4………(i)

ab=tanA.cotA=1…………(ii)

Therefore, (a+b)²=4²….(from i)

Therefore, a²+b²+2ab=16

Therefore, a²+b² =16–2..(from ii)

Therefore, a²+b² = 14……..(iii)

Let a²= A and b²= B

Therefore, A+B= 14(from iii)…….(iv)

Since, (A+B)³=A³+B³+3AB(A+B)

Therefore, A³+B³=(A+B)³-3AB(A+B)

Therefore, A³+B³=(14)³-3AB(14)

Therefore, A³+B³=2744–3a².b²(14)(from iv)

Therefore, (a²)³+(b²)³=2744–(ab)²42

Therefore, [(tanA)²]³+[(cotA)²]³=2744–1².42

Therefore, (tan²A)³+(cot²A)³=2744–42

Therefore, tan^6A+cot^6A=2702