sin20°.sec70+cos25°.cosec65=... a) 0 b) 1 c) 4 d) 2
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Given : sin20°.sec70°+cos25°.cosec65°
To Find : Value
a) 0
b) 1
c) 4
d) 2
Solution:
sin20°.sec70°+cos25°.cosec65°
Sec x = 1/Cosx
cosec x = 1/sinx
= sin20°/cos70°+cos25°/Sin65°
Sin ( 90° - x) = Cosx
Cos ( 90° - x) = Sinx
Cos 70° = Cos (90° - 20°) = Sin 20°
Sin65° = Sin ( 90° - 25°) = Cos 25°
= Sin 20° / Sin 20° + Cos 25°/Cos 25°
= 1 + 1
= 2
Hence sin20°.sec70°+cos25°.cosec65° = 2
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