Mathematics
Without using trigonometric tables, prove that:
sin2 20° + sin2 70° - tan2 45° = 0.
Trigonometrical Ratios
14 Likes
Answer
To prove,
sin2 20° + sin2 70° - tan2 45° = 0.
Solving, L.H.S. of the equation we get :
sin2 20° + sin2 70° - tan2 45°
We know that,
sin (90 - θ) = cos θ
and
sin2 θ + cos2 θ = 1.
⇒ sin2 20° + sin2 (90° - 20°) - (1)2
⇒ sin2 20° + cos2 20° - 1
⇒ 1 - 1
⇒ 0.
Since, L.H.S. = R.H.S.
Hence, proved that sin2 20° + sin2 70° - tan2 45° = 0.
Answered By
6 Likes