Prove that:- sin 10° *cos 75°*sec 80° *cosec 15 = 1
1 answer:
<em>Note</em><em>:</em><em> </em><em>You</em><em> </em><em>will</em><em> </em><em>need</em><em> </em><em>to</em><em> </em><em>write</em><em> </em><em>the</em><em> </em><em>degree</em><em> </em><em>symbol</em><em> </em><em>for</em><em> </em><em>the</em><em> </em><em>arguments</em><em> </em><em>of</em><em> </em><em>these</em><em> </em><em>trigonometric</em><em> </em><em>functions</em><em>.</em>
As sin(x)=cos(90-x), this means sin10 = cos80 and cos75=15.
So,
LHS = (cos80)(sec80)(sin15)(cosec15)
LHS = (cos 80)(1/cos 80)(sin 15)(1/sin 15)
LHS = 1
Therefore, the identity is true.
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