Question

Which of the following statements are true? Select all that apply. 2 answers

Answer 1

Given:

Given that a trigonometric statements.

Required:

To check whether the given statements are true or false.

Step-by-step explanation:

(A)

`\sin67\degree=\sin(42\degree+25\degree)`

Now, by using the formula

`\sin(42\degree+25\degree)=\sin42\degree\cos25\degree+\cos42\degree\sin25\degree`

Therefore, the option A is true.

(B)

`\tan(67)=\tan(70-3)`

Now, by using the formula,

`\tan(70-3)=(\tan70-\tan3)/(1+\tan70\tan3)`

Therefore, the option B is false.

(C)

`\cos67=\cos(41+26)`

Now, by using the formula

`\cos(41+26)=\cos41\cos26+\sin41\sin26`

Therefore, the option C is true.

(D)

`\tan67=\tan(23+44)`

Now by using the formula,

`\tan(23+44)=(\tan23+\tan44)/(1-\tan23.\tan44)`

Therefore, the option D is true.

(E)

`\sin67=\sin(81-14)`

Now, by using the formula

`\sin(81-14)=\sin81\cos14-\cos81\sin14`

Therefore, the option E is false.'

Final Answer:

The true statements are option A, C, and D.