cot70° + 4cos 70° is
Answers
Answer:
Step-by-step explanation:
cot70°+4cos70°
=cot(90°-20°)+4 cos(90°-20°)
=tan20°+4sin20°
=sin20°/cos20°+2×2.sin20°
=(sin20°+2×2sin20°.cos20°)/cos20°
=(sin20°+2.sin40°)/cos20°
=(sin20°+sin40°+sin40°)/cos20°
=(2.sin30°.cos10°+sin40°)/cos20°
=[2×1/2.cos(90°-80°)+sin40°]/cos20°
=[sin80°+sin40°]/cos20°
=[2sin60°.cos20°]/cos20°
=[2×(1/2).(3)^1/2.cos20°]/cos20°
=(3)^1/2 , Answer
Answer:
a=
3
Step-by-step explanation:
a=cot70
+4cos70
⇒a=cot(90
−20
)+4cos(90
−20
)
⇒a=tan20
+4sin20
[∵cot(90−θ)=tanθ,cos(90−θ)=sinθ]
⇒a=
cos20
sin20
+4sin20
cos20
⇒a=
cos20
sin20
+2sin40
=
cos20
sin20
+sin40
+sin40
⇒a=
cos20
2sin30
cos10
+cos(90
−40
)
[∵sinC+sinD=2sin
2
C+D
cos
2
C−D
]
⇒a=
cos20
cos10
+cos50
=
cos20
2cos30
cos20
[∵cosC+cosD=2cos
2
C+D
cos
2
C−D
]
⇒a=2×
2
3
⇒a=
3