Without using trigonometric table evaluate the following:\frac{\sin 50

1.	Without using trigonometric table evaluate the following:\frac{\sin 50^{\circ}}{\cos 40^{\circ}}+\frac{\operatorname{Cosec} 40^{\circ}}{\sec 50^{\circ}}-4 \cos 50^{\circ} \csc 40^{\circ}
Answer» sin 50° = sin( 90 - 40 ) = cos 50 ° Cosec 40 = Cosec ( 90 - 50 ) = sec 40° cos 50 = cos ( 90 - 40 ) = sin 40° sin 40 Cosec 40 = 1 ------------------------------------------- sin 50 / cos40 + Cosec 40 / sec50 - 4cos50cosec40 = cos 40 / cos 40 + sec 50/ sec 50 - 4sin 40 Cosec 40 = 1 + 1 - 4 = -2

Without using trigonometric table evaluate the following:\frac{\sin 50^{\circ}}{\cos 40^{\circ}}+\frac{\operatorname{Cosec} 40^{\circ}}{\sec 50^{\circ}}-4 \cos 50^{\circ} \csc 40^{\circ}

Answer»

sin 50° = sin( 90 - 40 ) = cos 50 °

Cosec 40 = Cosec ( 90 - 50 ) = sec 40°

cos 50 = cos ( 90 - 40 ) = sin 40°

sin 40 Cosec 40 = 1

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sin 50 / cos40 + Cosec 40 / sec50 - 4cos50cosec40

= cos 40 / cos 40 + sec 50/ sec 50 - 4sin 40 Cosec 40

= 1 + 1 - 4

= -2