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Question
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
Solution
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
⇒ `((sin47^circ)/(cos43^circ))^2 + (cos43^circ/sin47^circ)^2 - 4(1/sqrt(2))^2`
⇒ `(sin(90^circ - 43^circ)/cos43^circ)^2 + (cos(90^circ - 47^circ)/sin47^circ)^2 - 4(1/2)`
⇒ `(cos43^circ/cos43^circ)^2 + (sin47^circ/sin47^circ)^2 - 2`
⇒ 1 + 1 - 2 = 0
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