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# tan a + cot a = a then find the value of tan⁴a+cot⁴a=

Arun
25763 Points
3 years ago
[tan(a) + cot(a)]² = a2

tan²(a) + 2tan(a).cot(a) + cot²(a) = a2

tan²(a) + 2 + cot²(a) = a2

tan²(a) + cot²(a) = a2 – 2

[tan²(a) + cot²(a)]² =  (a2 – 2)2

tan^4(a) + 2tan²(a).cot²(a) + cot^4(a) = (a2 – 2)2

tan^4(a) + 2 + cot^4(a) = (a2 – 2)2

tan^4(a) + cot^4(a) = (a2 – 2)2 – 2 = (a4 + 4 – 2a2) – 2

tan^4(a) + cot^4(a) = a4 + 2 – 2a2
Nitin chowdhury
10 Points
3 years ago
tan a + tan b =a (tana + tanb)²= a²tan²a + 2 + cot²a =a²tana²+ cot²a = a²-2 (tana²+cota²)²=( a²-2)²tan⁴a +2+ cot⁴a = a⁴+4 -4a²". " =a⁴+4-2-4a²tan⁴a + cot⁴a = a⁴-4a²+2
Arun
25763 Points
3 years ago
sorry i have made a mistake in squaring,