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प्रश्न
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
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उत्तर
`(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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संबंधित प्रश्न
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`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
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`sinA/(1 - cosA) - cotA = cosecA`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
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`(sin theta + 1 - cos theta)/(cos theta - 1 + sin theta) = (1 + sin theta)/(cos theta)`
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\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
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Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
