Mathematics
Without using trigonometric tables, prove that:
cos2 25° + cos2 65° = 1
Trigonometrical Ratios
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Answer
To prove,
cos2 25° + cos2 65° = 1.
Solving, L.H.S. of the equation.
cos2 25° + cos2 65°
= cos2 25° + cos2 (90° - 25°)
As, cos (90° - θ) = sin θ
= cos2 25° + sin2 25°
= 1 [∵ cos2 θ + sin2 θ = 1]
Since, L.H.S. = R.H.S.
Hence, proved that cos2 25° + cos2 65° = 1.
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