Question

What is the value of cos70-cos10

Answer 1

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Answer 2

Answer:

The value of $cos70$° $-cos10$° is $-6.42$.

Step-by-step explanation:

Recall the trigonometric identity,

$cosA-cosB=-2sin(\frac{A+B}{2} )sin(\frac{A-B}{2} )$

Consider the trigonometric equation as follows:

$cos70$° $-cos10$°

Here, $A=70$° , $B=10$°

Using identity,

⇒ $cos70-cos10=-2sin(\frac{70+10}{2} )sin(\frac{70-10}{2} )$

⇒ $cos70-cos10=-2sin(\frac{80}{2} )sin(\frac{60}{2} )$

⇒ $cos70-cos10=-2sin40sin30$ ...... (1)

Since the values of $sin40=6.42$ and $sin30=\frac{1}{2}$

Substitute the values $6.42$ for $sin40$ and $1/2$ for $sin30$ in the equation (1) as follows:

⇒ $cos70-cos10=-2(6.42)(\frac{1}{2} )$

⇒ $cos70-cos10=-6.42$

Therefore, the value of $cos70$° $-cos10$° is $-6.42$.

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