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# Without Using Trigonometrical Tables, Evaluate: Cosec^2 57^@ - Tan^2 33^@ + Cos 44^@ Cosec 46^@ - Sqrt2 Cos 45^@ - Tan^2 60^@ - ICSE Class 10 - Mathematics

ConceptTrigonometry Problems and Solutions

#### Question

Without using trigonometrical tables, evaluate:

cosec^2 57^@ - tan^2 33^@ + cos 44^@ cosec 46^@ - sqrt2 cos 45^@ -  tan^2 60^@

#### Solution

cosec^2 57^@ - tan^2 33^@ + cos 44^@ cosec 46^@ - sqrt2 cos 45^@ -  tan^2 60^@

= cosec^2 (90^@ - 33^@)^@ - tan^2 33^@ + cos 44^@ cosec(90^@ - 44^@) - sqrt2 cos45^@ - tan^2 60^@

= sec^2 33^@ - tan^2 33^@ + cos 44^@ sec 44^@ - sqrt2 cos 45^@ - tan^2 60

= 1 + 1 - sqrt2 cos 45^@ -  tan^2 60

= 1+1 - sqrt2(1/(sqrt2)) - (sqrt3)^2

= 2 - 1 - 3

= - 2

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#### APPEARS IN

2015-2016 (March) (with solutions)
Question 2.2 | 4.00 marks

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Solution Without Using Trigonometrical Tables, Evaluate: Cosec^2 57^@ - Tan^2 33^@ + Cos 44^@ Cosec 46^@ - Sqrt2 Cos 45^@ - Tan^2 60^@ Concept: Trigonometry Problems and Solutions.
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