Question

If tan A = cot A then prove that sin a + cos A = √2

Answer 1

Solution

→ tanA = cotA

Since tan A = 1/cot A

→ 1/cot A = cot A

→ 1 = cot²A

→ 1 = cot A

Hence value of A is 45°.

L.H.S → sinA + cosA

→ sin 45° + cos 45°

We know that:

• sin 45° = cos 45° = √2/2

→ √2/2 + √2/2

→ 2√2/2 = √2 = R.H.S

Hence Proved

Answer 2

$\huge{\mathfrak{</p><p><strong>Answer:</strong></p><p>}}$

$\huge{\bf{Given :-}}$

$\large{\sf{tan A \:=\:cot A}}$

$\huge{\bf{We \: know \: that }}$

$\huge{\boxed{tan A \:=\:1/cot A}}$

$\large{\sf{ 1 = (cot × Cot)A}}$

$\large{\sf{1 \:=\:cot A}}$

$\huge{\boxed{Value \:of\:A \:is 45^{\circ}}}$

$\huge{\boxed{L.H.S \:=\:sin 45^{\circ} + cos 45^{\circ}}}$

sin 45°= cos 45° = √2/2

√2/2 + √2/2

2√2 / 2

√2 =R. H. S

$\huge{\boxed{Hence \:\:Proved}}$