Answer: a)2(cos 2 45 ∘ +tan 2 60 ∘ )−6(sin 2 45 ∘ −tan 2 30 ∘ ) =2[( 2 1 ) 2 +( 3 ) 2 ]−6[( 2 1 ) 2 −( 3 1 ) 2 ] =2[ 2 1 +3]−6[ 2 1 − 3 1 ] =2[ 2 7 ]−6[ 6 3−2 ] =7−1=6 b)2(cos 4 60 ∘ +sin 4 60 ∘ )−(tan 2 60 ∘ +cos 2 45 ∘ )+3sec 2 30 ∘ =2[( 2 1 ) 4 +( 2 1 ) 4 ]−[( 3 ) 2 +( 2 1 ) 2 ]+3× 3 4 =2[ 16 1 + 16 1 ]−[3+ 2 1 ]+4 =2× 16 2 +4− 2 7 = 4 1 +4− 2 7 = 4 1+16−14 = 4 3 Reply
Answer:
a)2(cos
2
45
∘
+tan
2
60
∘
)−6(sin
2
45
∘
−tan
2
30
∘
)
=2[(
2
1
)
2
+(
3
)
2
]−6[(
2
1
)
2
−(
3
1
)
2
]
=2[
2
1
+3]−6[
2
1
−
3
1
]
=2[
2
7
]−6[
6
3−2
]
=7−1=6
b)2(cos
4
60
∘
+sin
4
60
∘
)−(tan
2
60
∘
+cos
2
45
∘
)+3sec
2
30
∘
=2[(
2
1
)
4
+(
2
1
)
4
]−[(
3
)
2
+(
2
1
)
2
]+3×
3
4
=2[
16
1
+
16
1
]−[3+
2
1
]+4
=2×
16
2
+4−
2
7
=
4
1
+4−
2
7
=
4
1+16−14
=
4
3