without using table evaluate 2 tan 60° sin 60° + tan 39° - cot 57°
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Answer:
$$\dfrac{sec \, 39^{\circ}}{coses \, 51^{\circ}} \, + \, \dfrac{2}{\sqrt{3}}tan \, 17^{\circ} \, tan \, 38^{\circ} \, tan \, 60^{\circ} \, tan \, 52^{\circ} \, tan \, 73^{\circ} \, - \, 3(sin^ \, 31^{\circ} \, + \, sin^2 \, 59^{\circ})$$
=
cosec(90
∘
−39
∘
)
sec39
∘
+
3
2
tan17
∘
tan38
∘
tan60
∘
tan(90
∘
−38
∘
)tan(90
∘
−17
∘
)−3(sin
2
31
∘
+sin
2
(90
∘
−31
∘
)
=
sec39
∘
sec39
∘
+
3
2
tan17
∘
tan38
∘
tan60
∘
cot38
∘
cot17
∘
−3(sin
2
31
∘
+cos
2
31
∘
)
=
sec39
∘
sec39
∘
+
3
2
tan60
∘
−3(sin
2
31
∘
+cos
2
31
∘
)
=1+
3
2
×
3
−3×1=1+2−3=0
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