Question

Given
tanø =2-√3,
TO PROVE
tan^3ø + cot^3ø -2=50​

Answer 1

Step-by-step explanation:

tanA=2-√3

1/tanA=2+√3....... on rationalisation

cotA=2+√3

Let 2+√3 be x. 2-√3 be 1/x

(2+√3)³+(2-√3)³

x³+1/x³

(x+1/x)(x²+1/x²-(x)(1/x))

(x+1/x)(x²+1/x²-1)

(2+√3+2-√3)((2+√3+2-√3)²-2-1)

4(4²-3)

4(16-3)

4(13)

52

tan³A+cot³A=(2-√3)³+(2+√3)³

tan³A+cot³A=52

tan³A+cot³A-2=50

hence proved

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