Question

2 MARKS:
If cos (A-B) = sin (A+B) = 1, then find the value of A and B​

Answer 1

Step-by-step explanation:

2marks or marks for 10th class

Answer 2

$\sf{Answer}$

Given :-

• cos(A - B ) = 1
• sin ( A + B ) = 1

To find :-

• Value of A,B

Solution:-

Take two conditions

cos ( A - B ) = 1

We know that cos 0 = 1

So,

cos ( A - B ) = cos0

Removing cos on both sides

A - B = 0 -------- eq 1

sin ( A + B ) = 1

We know that sin90 = 1

So,

sin ( A + B ) = sin 90°

Removing sin on both sides

A + B = 90° ------ eq 2

Adding two equations

A - B + A + B = 0+ 90

A + A -B + B = 90°

2A = 90°

A = 90°/2

A = 45°

Substitute in eq 2

A + B = 90°

45 + B = 90°

B = 90°-45°

B = 45°

So, the values of A,B are 45°,45°

_________________

Know more:-

cos(A + B) = cosAcosB - sinAsinB

cos ( A - B) = cosA cosB + sinAsinB

tan ( A +B ) = tanA + tanB / 1 - tanAtanB

tan( A-B) = tanA - tanB/1 + tanAtanB

cot ( A + B ) = cotBcotA -1 / cotB + cotA

cot ( A - B ) = cotB cotA + 1/ cotB - cotA

tan(45+ A) = 1+tanA/1 - tanA

tan (45 - A ) = 1-tanA/1 + tanA

Trignometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trignometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trignometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj