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Evaluate Without Using Trigonometric Tables: `Cos^2 26^@ + Cos 64^@ Sin 26^@ + (Tan 36^@)/(Cot 54^@)` - Mathematics

Evaluate without using trigonometric tables:

`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`

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Solution

`cos^2 26^@ + cos 64^@ sin 26^@ + tan 36^@/cot 54^@`

`= cos^2 26^@ + cos(90^@ - 26^@) sin 26^@ + tan 36^@/(cot(90^@ - 36^@))`

`= cos^2 26^@ + sin 26^@.sin26^@ + tan36^@/tan36^@`      `[∵ cos(90^@ - theta) = sin theta, cot(90^@ -  theta) = tan theta]`

`= cos^2 26^@ + sin^2 26^@ + 1`

`= 1 + 1          [∵ cos^2 theta + sin^2 theta = 1]`

= 2

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