Question

If cos 3A = sin(A-34), where 3A is an acute angle, then find @

Answer 1

$\bf{\underline{\underline{\bf{\red{Question}}}}}$

If cos 3A = sin(A-34), where 3A is an acute angle, then find the value of A

$\bf{\underline{\underline{\bf{\red{To\:find}}}}}$

Find the value of A

$\bf{\underline{\underline{\bf{\red{Solution}}}}}$

$\large\implies\sf cos3A=sin(A-34)$

$\large\implies\sf sin(90-3A)=sin(A-34)$

$\large\implies\sf 90-3A=A-34$

$\large\implies\sf 90+34=3A+A$

$\large\implies\sf 124=4A$

$\large\implies\sf A=\large\cancel\frac{116}{4}=31$

$\large{\boxed{\mathrm{A=31}}}$

$\bf{\underline{\underline{\bf{\red{Important\:notes}}}}}$

• sin(90-∅) = cos∅
• tan(90-∅) = cot∅
• sec(90-∅) = cosec∅
• sin²∅+cos²∅ = 1
• tan²∅-cot²∅ = 1
• cosec²∅-cot²∅ = 1

Answer 2

$\bold{\huge{\fbox{\color{Black}{Given}}}}$

Cos3A = sin(A-34)

$\bold{\huge{\fbox{\color{Black}{To find}}}}$

Value of A

$\bold{\huge{\fbox{\color{Black}{Solution}}}}$

We know that,

Sin(90-Φ) = CosΦ

So,

=> Cos3A = sin(A-34)

=> Sin(90-3A) = sin(A-34)

On Dividing both sides by sin, we get

=> (90 - 3A) = ( A - 34)

=> 90 + 34 = A + 3A

=> 124 = 4A

=> A = 124/4 = 31°

Some more equation :-

• Sin( 90 - Φ) = CosΦ

• Cos(90 -Φ) = SinΦ

• Sec(90-Φ) = CosecΦ

• Cosec(90-Φ) = SecΦ

• Tan(90-Φ) = CotΦ

• Cot(90-Φ) = TanΦ