Question

prove that cos 70 degree by sin 20 degree +cos 55 degree into cos 45 degree by 15 degree into tan 25 degree into tan 65 degree into tan 85 degree is equals to 2

Answer 1

Make the question more specific

Answer 2

Answer:

To Prove:

$\frac{cos\,70^{\circ}}{sin\,20^{\circ}}+\frac{cos\,55^{\circ}\times cosec\,45^{\circ}}{tan\,5^{\circ}\times tan\,25^{\circ}\times tan\,65^{\circ}\times tan\,85^{\circ}}=2$

Consider,

$LHS\,=\,\frac{cos\,70^{\circ}}{sin\,20^{\circ}}+\frac{cos\,55^{\circ}\times cosec\,45^{\circ}}{tan\,5^{\circ}\times tan\,25^{\circ}\times tan\,65^{\circ}\times tan\,85^{\circ}}$

$=\,\frac{cos\,(90-70)^{\circ}}{sin\,20^{\circ}}+\frac{cos\,(90-45)^{\circ}\times cosec\,45^{\circ}}{tan\,(90-85)^{\circ}\times tan\,(90-65)^{\circ}\times tan\,65^{\circ}\times tan\,85^{\circ}}$

$=\,\frac{sin\,70^{\circ}}{sin\,20^{\circ}}+\frac{sin\,45^{\circ}\times cosec\,45^{\circ}}{cot\,85^{\circ}\times cot\,65^{\circ}\times tan\,65^{\circ}\times tan\,85^{\circ}}$

$=\,\frac{1}{1}+\frac{1}{cot\,85^{\circ}\times tan\,85^{\circ}\times cot\,65^{\circ}\times tan\,65^{\circ}}$

$=\,\frac{1}{1}+\frac{1}{1\times1}$

$=\,1+1$

$=\,2$

$=\,RHS$

Hence Proved