Question

show that tan10°tan20°tan70°tan80°=1​
all steps needed

Answer 1

tan 10 = tan (45-35)

tan 20= tan(45-25)

tan 70 = tan (45+25)

tan 80=tan (45+35)

we know that

tan (x-y) tan (x+y) = 1

So, tan (20) xtan (70)=1

tan (10) xtan (80) = 1

=1x1 = 1

Answer 2

Answer:

Step-by-step explanation:

tan 10 .tan 20 .tan 70. tan 80=1

it is same as:-

tan10. tan80. tan20 .tan70=1

LHS:-

tan10. tan80. tan20 .tan70

tan (90-10).tan80.tan (90-20).tan70

cot80.tan80.cot70 . tan70

1×1

=1

=RHS

HENCE PROVED