Question

please solve this problem​

Answer 1

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

We have to find out the value of cos 45°.

Formula:

$\dag\underline{\boxed{\tt \cos(x) = \sqrt{ \dfrac{1 + \cos(2x) }{2} } }}$

So, we know that,

→ cos 90° = 0

So,

$\tt \implies \cos(45^{\circ} ) = \sqrt{ \dfrac{1 + \cos(2 \times 45^{\circ} ) }{2}}$

$\tt \implies \cos(45^{\circ} ) = \sqrt{ \dfrac{1 + \cos(90^{\circ} ) }{2}}$

$\tt \implies \cos(45^{\circ} ) = \sqrt{ \dfrac{1 + 0}{2}}$

$\tt \implies \cos(45^{\circ} ) = \sqrt{ \dfrac{1}{2}}$

$\tt \implies \cos(45^{\circ} ) = \dfrac{1}{ \sqrt{2} }$

★ So, the value of cos 45° is 1/√2.

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• cos 45° = 1/√2.

$\texttt{\textsf{\large{\underline{Additionals}:}}}$

1. Relationship between sides.

• 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) and vice versa.
• cosec(90° - x) = sec(x) and vice versa.
• tan(90° - x) = cot(x) and vice versa.

•••♪