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Byju's Answer
Standard XII
Mathematics
Basic Inverse Trigonometric Functions
Prove thatsin...
Question
Prove that
sin
6
x .- tan
6
x - 3 sec
2
x •
tan
2
x = 1
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Solution
It should be sec instead of sin
As,
a³-b³a³-b³=(a-b)³+3ab(a-b)
And, 1+tan
²x=sec²x
(sec
²x)³-(tan²x)³
=(sec²x-tan²x)³+3sec²xtan²x(sec²x-tan²x)
=1+3sec²xtan2x(1)
=1+3tan²xsex²x-3tan²xsex²x
=1
hence proved
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