Question

Sin20/cos70 + cos20/sin70 +tan20tan70

Answer 1

Answer:

Step-by-step explanation:

sin 20°/cos 70° + cos 20°/sin 70° + tan 20° X tan 70°

sin (90° - 70°)/cos 70° + cos (90° - 70°)/sin 70° + tan (90° - 70°) X tan 70°

cos 70°/cos 70° + sin 70°/sin 70° + cot 70° X tan 70°

1 + 1 + (1/tan 70° X tan 70°)

2 + 1

3

Answer 2

Answer:

$\frac{Sin20}{Cos70} +\frac{Cos20}{Sin70}+ Tan20*Tan70$.....(a)

We know that:

1. Sin20=cos(90-20)=cos(70)
2. Cos20=sin(90-20)=sin(70)
3. Tan20=cot(90-20)=cot(70)

Substitute 1., 2. and 3. in (a):

$\frac{Cos70}{Cos70} +\frac{Sin70}{Sin70}+ cot70*Tan70$

We know that cot∅*tan∅=1

Thus, cot70*tan70=1.

$\frac{Cos70}{Cos70} +\frac{Sin70}{Sin70}+ cot70*Tan70=1+1+1=3$

Thus 3 is your answer.

HOPE THIS HELPS :D