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# Without Using Trigonometric Tables Evaluate: (Sin 65^@)/(Cos 25^@) + (Cos 32^@)/(Sin 58^@) - Sin 28^2. Sec 62^@ + Cosec^2 30^2 - ICSE Class 10 - Mathematics

ConceptTrigonometric Ratios of Complementary Angles

#### Question

Without using trigonometric tables evaluate:

(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@

#### Solution

(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@

= (sin(90^@ - 25^@))/cos 25^@ + (cos (90^@  - 58^@))/sin 58^@  - sin 28^@ xx 1/(cos(90^@ - 28^@) ) + 1/sin^2 30

= cos 25^@/cos 25^@  + (sin 58^@)/(sin 58^@) - sin 28^@ xx 1/sin 28^@ + (1/(1/2)^2)

= 1 + 1 - 1 + 4

= 5

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 1.3 | 4.00 marks
Solution Without Using Trigonometric Tables Evaluate: (Sin 65^@)/(Cos 25^@) + (Cos 32^@)/(Sin 58^@) - Sin 28^2. Sec 62^@ + Cosec^2 30^2 Concept: Trigonometric Ratios of Complementary Angles.
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