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Question

Without using trigonometric tables, evaluate:

(i)cos 48sin 42

(ii)cosec 31sec 59

(iii)cot 34tan 56

(iv)cos2 13sin2 77 [4 MARKS]

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Solution

Solution: 1 Mark each

(i)cos 48sin 42=cos(9042)sin 42

=sin 42sin 42=0

[cos(90θ)=sin θ]


(ii)cosec 31sec 59=cosec(9059)sec 59

=sec 59sec 59=0

[cosec(90θ)=sec θ]


(iii)cot 34tan 56=cot(9056)tan 56

=tan 56tan 56=0

[cot(90θ)=tan θ]


(iv)cos2 13sin2 77=cos2 (9077)sin2 77

=sin2 77sin2 77=0

[cos(90θ)=sin θ]


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