Mathematics
Without using trigonometric tables, evaluate the following:
(cos2 25° + cos2 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).
Trigonometric Identities
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Answer
We need to find the value of,
(cos2 25° + cos2 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).
The above equation can be written as,
⇒ [cos2 25° + cos2 (90 - 25)°] + cosec θ cosec θ - cot θ cot θ
⇒ (cos2 25° + sin2 25°) + cosec θ cosec θ - cot θ cot θ
⇒ 1 + cosec2 θ - cot2 θ
⇒ 1 + 1
⇒ 2.
Hence, the value of the equation is 2.
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