Sin 50/Cos 40 + Cosec 40/ Sec 50 - 4 cos 50× cosec 40 (please)
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Answer:
We know that,
cos(90−θ)=sinθ
sec(90−θ)=cosecθ
cosecθ=
sinθ
1
Therefore,
cos40
∘
=cos(90
∘
−50
∘
)=sin50
∘
sec50
∘
=tan(90
∘
−40
∘
)=cosec40
∘
cos50
∘
=sin(90
∘
−40
∘
)=sin40
∘
To evaluate,
cos40
∘
sin50
∘
+
sec50
∘
csc40
∘
−4cos50
∘
cosec40
∘
=
sin50
∘
sin50
∘
+
cosec40
∘
cosec40
∘
−4(
sin40
∘
cos50
∘
)
=1+1−4(
sin40
∘
sin40
∘
)
=1+1−4
=−2
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