Question

3. Prove that:
(1) tan 20° tan 35º tan 45º tan 55° tan 70° = 1
(2) cos80°/Sin 10° + cos 59° cosec 31° = 2​

Answer 1

Answer:

first ans is 1

Step-by-step explanation:

tan20 tan70 tan35 tan55 tan45

tan20 tan (90 - 20) tan35 tan (90-35) tan45

tan20 cot20 tan35 cot35 tan45

1 *1*1

1

proved

Answer 2

Solution

(1)

L.H.S.=tan 20° tan 35º tan 45º tan 55° tan 70°

=(tan20°tan 70°)(tan45°)(tan35°tan55°)

=(tan20°cot(90°-70°))(1)(tan35°cot(90°-55°))

=(tan20°cot20°)(tan35°cot35°)

=1×1=1=R.H.S(proved)

(2)

L.H.S.=cos80°/Sin 10° + cos 59° cosec 31°

=[cos80°/cos(90°-10°)]+cos59°sec(90°-31°)

=(cos80°/cos80°)+cos59°sec59°

=1+1

=2=R.H.S.(proved)