Question

5. If tano+ coto= 5, find the value of tan^{2}o-cot^{2}o

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Answer 1

$\large\bf{\underline\orange{Answer \:↝}}$

Que :- If TanO + CotO = 5, Find the value of Tan²O - Cot²O.

Ans :- Given,

TanO + CotO = 5

(Squaring both side)

(TanO + CotO)² = (5)²

tan²O + cot²O + 2× tanO×cotO = 25

[ (a+b)² = a²+b²+2ab ]

tan²O+ cot²O+ 2×1 = 25

(tanO×cotO = tanO×1/tanO = 1)

tan²O + cot²O = 25 - 2 = 23

Hence Tan²O - Cot²O = 23

Answer 2

$\huge\bf{\underline\red{Answer \: ⇝}}$

TanO + CotO = 5

(Squaring both side)

(TanO + CotO)² = (5)²

tan²O + cot²O + 2× tanO×cotO = 25

[ (a+b)² = a²+b²+2ab ]

tan²O+ cot²O+ 2×1 = 25

(tanO×cotO = tanO×1/tanO = 1)

tan²O + cot²O = 25 - 2 = 23

Hence Tan²O - Cot²O = 23