Need help with a couple of Trig Q's please.

Just a couple I can't work out from the P2 book;

1.) Simplify: 4sin6θ sin4θ + 4cos6θ cos4θ

2.) Find exact value (without a calculator) of: (2tan67½) / (1-tan²67½)

Many thanks.

Reply 1

Fermat

Slice'N'Dice

Just a couple I can't work out from the P2 book;

1.) Simplify: 4sin6θ sin4θ + 4cos6θ cos4θ

Let A = 6θ
Let B = 4θ

giving

4(sinA.sinB + cosA.cosB)
4.cos(A-B)
4.cos(2&#952 :wink:

========

Reply 2

Fermat

Slice'N'Dice

Just a couple I can't work out from the P2 book;

2.) Find exact value (without a calculator) of: (2tan67½) / (1-tan²67½)

Many thanks.

67½ = 90 - 45/2
let θ = 90 - 45/2

2tanθ / (1 - tan²&#952 :wink:

2.sinθ.cosθ / (cos²θ - sin²&#952 :wink:

sin2θ / cos2θ
(sin180cos45 - cos180sin45) / (cos180cos45 + sin180sin45)
(1/√2) / (-1/√2)
-1
==

Reply 3

Cille

Or use tan 2A = (2tanA)/[1- tan^2(A)]

A=67.5 => tan2A = tan135 = - tan45 = -1

Reply 4

Fermat

nollaig

Or use tan 2A = (2tanA)/[1- tan^2(A)]

A=67.5 => tan2A = tan135 = - tan45 = -1

I couldn't remember that identity :redface:

, That's why I did it the long way :cool:

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