S
Evaluate
sin (-660) sec (420)/cos(225) cos(510)
Answers
Answer:
sin(−660°)tan(1050°)sec(−420°)
=
cos(225°)cosec(315°)cos(510°)
−sin(660°)tan(1050°)sec(−420°)
=
cos(×180
∘
+45°)cosec(2×180
∘
−45°)cos(3×180
∘
−30°)
−sin(4×180
∘
−60°)tan(6×180
∘
−30°)sec(2×180
∘
+60°)
=
cos(π+45°)cosec(2π−45°)cos(3π−30°)
−sin(4π−60°)tan(6π−30°)sec(2π+60°)
=
−cos45°(−cosec45°)(−cos30°)
sin60°(−tan30°)sec60°
=
2
1
×−
2
×−
2
3
2
3
×(
3
−1
)×2
=
3
2
Hence, the answer is
3
2
.
Step-by-step explanation:
sin(−660°)tan(1050°)sec(−420°)
=
cos(225°)cosec(315°)cos(510°)
−sin(660°)tan(1050°)sec(−420°)
=
cos(×180
∘
+45°)cosec(2×180
∘
−45°)cos(3×180
∘
−30°)
−sin(4×180
∘
−60°)tan(6×180
∘
−30°)sec(2×180
∘
+60°)
=
cos(π+45°)cosec(2π−45°)cos(3π−30°)
−sin(4π−60°)tan(6π−30°)sec(2π+60°)
=
−cos45°(−cosec45°)(−cos30°)
sin60°(−tan30°)sec60°
=
2
1
×−
2
×−
2
3
2
3
×(
3
−1
)×2
=
3
2
Hence, the answer is
3
2
.