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Find the value of :A. `sin 74^(@)`B. `cos 106^(@)`C. `sin 15^(@)`D. `cos 75^(@)` |
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Answer» Correct Answer - D (i) `sin 74^(@)=sin (2xx37^(@))=2 sin 37 cos 37^(@)=2(3/5)(4/5)=24/25` (ii) `cos 106^(@)=cos (2xx53^(@))=cos^(2) 53^(@)-sin^(2) 53^(@)=(3/5)^(2)-(4/5)^(2)=(9-16)/25=7/25` (iii) `sin 15^(@)=sin (45^(@)-30^(@))=sin 45^(@) cos 30^(@)-cos 45^(@) sin 30^(@)=1/sqrt(2)xxsqrt(3)/2-1/sqrt(2)xx1/2=(sqrt(3)-1)/(2sqrt(2))` (iv) `cos 75^(@)=cos(45^(@)+30^(@))=cos 45^(@) cos 30^(@)-sin 45^(@) sin 30^(@)=1/sqrt(2)xxsqrt(3)/2-1/sqrt(2)xx1/2=(sqrt(3)-1)/(2sqrt(2))` |
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