Question

the value of sin48° cos42° + cos48° sin42° =​

Answer 1

Hello,Buddy!!

Refer The Attachment ⤴️

• $\sin(48) \cos(42) + \cos(48) \sin(42) = 1$

@MrMonarque♡

Hope It Helps You ✌️

Answer 2

$\textsf{\large{\underline{Solution}:}}$

We have to evaluate the given expression.

= sin 48° cos 42° + cos 48° sin 42°

We know that:

→ sin(90° - α) = cos α

→ cos(90° - α) = sin α

Therefore, the expression becomes:

= sin 48° cos (90° - 48°) + cos 48° sin(90° - 48°)

= sin 48° × sin 48° + cos 48° × cos 48°

= sin² 48° + cos² 48°

= 1 [As sin²α + cos²α = 1]

Therefore:

→ sin 48° cos 42° + cos 48° sin 42° = 1

Alternative Method:

We know that:

→ sin(α + β) = sin α cos β + cos α sin β

Take α = 48° and β = 42°, we get:

→ sin(48° + 42°) = sin 48° cos 42° + cos 48° sin 42°

→ sin 90° = sin 48° cos 42° + cos 48° sin 42°

→ sin 48° cos 42° + cos 48° sin 42° = 1

Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

1. Relationship between sides and T-Ratios.

• sin(x) = Height/Hypotenuse.
• cos(x) = Base/Hypotenuse.
• tan(x) = Height/Base.
• cot(x) = Base/Height.
• sec(x) = Hypotenuse/Base.
• cosec(x) = Hypotenuse/Height.

2. Square formulae.

• sin²x + cos²x = 1.
• cosec²x - cot²x = 1.
• sec²x - tan²x = 1

3. Reciprocal Relationship.

• sin(x) = 1/cosec(x)
• cos(x) = 1/sec(x)
• tan(x) = 1/cot(x)

4. Cofunction identities.

• sin(90° - x) = cos(x)
• cos(90° - x) = sin(x)
• cosec(90° - x) = sec(x)
• sec(90° - x) = cosec(x)
• tan(90° - x) = cot(x)
• cot(90° - x) = tan(x)