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Without Using Trigonometric Tables Evaluate (Sin 35^@ Cos 55^@ + Cos 35^@ Sin 55^@)/(Cosec^2 10^@ - Tan^2 80^@) - Mathematics

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Question

Without using trigonometric tables evaluate

`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`

Solution

`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80)`

`= (sin 35^@ . cos (90^@ - 35^@) + cos 35^@. sin (90^@ - 35^@))/(cosec^2(90^@ - 80^@) - tan^2 80^@`)

`= (sin 35^@ . sin 35^@ + cos 35^@ . cos 35^@) /(sec^2 80^@ - tan^2 80^@)`

`= (sin^2 35^@ + cos^2 35^@)/(sec^2 80^@ - tan^2 80^@) = 1/1 = 1`

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APPEARS IN

 2009-2010 (March) (with solutions)
Question 3.2 | 3.00 marks
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Without Using Trigonometric Tables Evaluate (Sin 35^@ Cos 55^@ + Cos 35^@ Sin 55^@)/(Cosec^2 10^@ - Tan^2 80^@) Concept: Trigonometric Identities.
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