Question

tan15°*tan20°*tan70°*tan75°
Best Answer will be marked as Brainliest​

Answer 1

tan(15o)

=tan(45o−30o)

As,

tan(A−B)=tan(A)−tan(B)1+tan(A)tan(B)

So,

tan(15o)=tan(45o)−tan(30o)1+tan(45o)tan(30o)

As, we know,

tan(45o)=1

tan(30o)=13√

So,

tan(15o)=1−13√1+13√

=3√−13√3√+13√

=3√−13√+1

=(3√−1)2(3√+1)(3√−1)

=3−23√+13−1

=4−23√2

⟹tan(15o)=2−3–√

Similarly,

tan(75∘)

=tan(45∘+30∘)

As,

tan(A+B)=tan(A)+tan(B)1−tan(A)tan(B)

So,

tan(75∘)=tan(45∘)+tan(30∘)1−tan(45∘)tan(30∘)

As, we know,

tan(45∘)=1

tan(30∘)=13√

So,

tan(75∘)=1+13√1−13√

=3√+13√3√−13√

=3√+13√−1

=(3√+1)2(3√−1)(3√+1)

=3+23√+13−1

=4+23√2

⟹tan(75∘)=2+3–√

Values of tan(20∘) and tan(70∘) cannot be found out simple analytically.

Here I have addresses of videos which explain in full how to find the value of tan(15∘) and tan(75∘).

Answer 2

Answer:

1

Step-by-step explanation:

tan 15° tan 20° tan 70° tan 75°

{∴ tan(90 - Ф) = cot Ф}

⇒ tan(90 - 75) tan 20° tan(90 - 20) tan 75°

⇒ cot 75° tan 20° cot 20° tan 75°

⇒ (1/tan 75°) tan 20° (1/tan 20°) tan 75°

{∴ 1/tanФ = cotФ}

⇒ 1

Hope it helps!