Question

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show that


`1 + \tan ^(2)({ (2\pi)/(3) }) = \sec^(2)( { (2\pi)/(3) }) \:`




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Answer 1

Explanation:

note :

tanx = sinx/cosx and secx = 1/cosx

1+tan²(2π/3) = 1+(sin2π/3/cos2π/3)²

= 1 +( sin2π/3)²/(cos2π/3)²

=( sin2π/3)²+(cos2π/3)²/(cos2π/3)²

but : ( sin2π/3)²+(cos2π/3)²=1

so :1+tan²(2π/3) = 1 /(cos2π/3)²

=( 1/cos2π/3)²

:1+tan²(2π/3) =sec²( 2π/3)