Question

Cos 25°cos35°-sin10°sin20°​

Answer 1

Step-by-step explanation:

Cos 25°cos35°-sin10°sin20°

={Cos(25+35)°+Cos(25-35)°}÷2-{Cos(10-20)-Cos(10+20)}÷2

={Cos 60°+Cos(-10°)}÷2-{cos(-10°)-Cos(30°)}÷2

=Cos 60°/2+Cos10°/2-Cos10°/2+Cos30°/2

=(1/2)÷2+0+(√3/2)÷2

=1/4+√3/4=(1+√3)/4

Answer 2

The value of Cos 25°cos35°-sin10°sin20°​ is $\frac{\sqrt{3 }+1 }{4}$

Step-by-step explanation:

W know that,

2cosA cos B = cos(A +B) + cos (A - B)

2sinA sin B = cos(A - B)  - cos (A + B)

Rewrite the equation as,

⇒ 1/2 [2cos 25°cos35°-2sin10°sin20°​]

cos(A +B)  = cos(25+35)

= cos60

cos (A - B) = cos (25 - 35)

= cos (10)

⇒1/2 [2cos 25°cos35°-2sin10°sin20°​]

⇒ 1/2 [ 1/2 + cos 10° - cos10° + √3/2]

⇒ $\frac{1}{2} [\frac{1+\sqrt{3} }{2} ]$

⇒  $\frac{\sqrt{3 }+1 }{4}$

Final answer:

The value of Cos 25°cos35°-sin10°sin20°​ is $\frac{\sqrt{3 }+1 }{4}$

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