Question

Prove that tan square 30degree+tan square 45degree+tan square 60degree=13 upon 3

Answer 1

Hey dear friend

Tan²30°+Tan²45°+Tan²60°=13/3

Tan30°=1/✓3
Tan45°=1
Tan60°=✓3
Substituting all values

=>(1/✓3)²+(1)²+(✓3)²
=>1/3+1+3
=>1+3+9/3
=>13/3

13/3=R.H.S.

Hence Proved

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Answer 2

LHS = tan²A - sin²A

= ( sin²A/cos²A ) - sin²A

= sin²A [ 1/cos²A - 1 ]

= sin²A( sec²A - 1 )

= sin²A tan²A

[ since , sec²A - 1 = tan²A ]

= tan²Asin²A

= RHS