Question

find the value of sin 50 degree/ cos 40 degree + cosec 40 degree/ sec 50 degree -4 cos 50 degree cosec 40 degree

Answer 1

Hi ,

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

I hope this helps you.

:)

Answer 2

Answer:

LHS=(sin10+sin50)+(sin20+sin40)

=(2sin 30cos 20)+(2sin 30cos 10)

=2sin 30(cos10+cos20)

=2×1/2 (sin80+sin70)

=sin70+sin80=RHS