cos²60° + cos²30° + tan76° x tan14° - 2 = ?
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Step-by-step explanation:
Let cos
2
76
∘
+cos
2
16
∘
−cos76
∘
cos16
∘
=I
I=cos
2
(60
∘
+16
∘
)+cos
2
16
∘
−cos(60
∘
+16
∘
)cos16
∘
Using cos(A+B)=cosAcosB−sinAsinB
I=(cos60
∘
cos16
∘
−sin60
∘
sin16
∘
)
2
+cos
2
16
∘
−(cos60
∘
cos16
∘
−sin60
∘
sin16
∘
)cos16
∘
=
4
cos
2
16
∘
+
4
3sin
2
16
∘
−
2
3
cos16
∘
sin16
∘
+cos
2
16
∘
−
2
cos
2
16
∘
+
2
3
cos16
∘
sin16
∘
=
4
3cos
2
16
∘
+
4
3sin
2
16
∘
=
4
3
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