Question

show that Cos70°. Cos10°+ Sin70°. Sin10° =1/2

Answer 1

Answer:

Cos 70 . Cos 10 + Sin 70 . Sin 10 = 1/2

LHS:-

This is of the form: Cos A.Cos B + Sin A.Sin B, which is actually Cos ( A-B ).

Here, A = 70, B = 10

Hence we can write it as:

⇒ Cos ( 70 - 10 )  

⇒ Cos 60

Cos 60 is actually 1/2.

Hence LHS = RHS

Hence Proved !!

Answer 2

The answer to this question is proved and explained below:

Given:

Cos70°. Cos10°+ Sin70°. Sin10° = $\frac{1}{2}$

To Prove:

• LHS = RHS
• Left Hand side = Right hand side

Solution:

LHS =

Cos70°. Cos10°+ Sin70°. Sin10° is similar to, Cos A.Cos B + Sin A.Sin B

According to the formula, Cos A.Cos B + Sin A.Sin B = Cos ( A-B ).

Here, A = 70, B = 10

Hence it can be written as,

Cos70°. Cos10°+ Sin70°. Sin10° = Cos ( 70 - 10 )  

= Cos 60

= 1 / 2

= RHS

The value of cos60 is nothing but  $\frac{1}{2}$

Hence it is proved that, LHS = RHS

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