Question

4. II SOVU
P, C
U
MIC are on a
3. If a sins + b cosr=cb sinʼy + a cosy = d.
a tanx-b tany, then proven
a²_ (d-a)(c-a)
62 (6-c)(b-d​

Answer 1

Answer:

9

Step-by-step explanation:

Given :-

→ a sin∅ + b cos∅ = c .......(1) .

Now,

→ ( a sin∅ + b cos∅ )² + ( a cos∅ - b sin∅ )² .

= a²sin²∅ + b²cos²∅ + 2a sin∅ b cos∅ + a²cos²∅ + b²sin²∅ - 2a sin∅ b cos∅ .

= a²sin²∅ + a²cos²∅ + b²cos²∅ + b²sin²∅ .

= a²( sin²∅ + cos²∅ ) + b²( cos²∅ + sin²∅ ) .

= a² + b² . [ ∵ sin²∅ + cos²∅ = 1 ] .

Thus, ( a sin∅ + b cos∅ )² + ( a cos∅ - b sin∅ )² = ( a² + b² ) .

⇒ c² + ( a cos∅ - b sin∅ )² = ( a² + b² ) .

⇒ ( a cos∅ - b sin∅ )² = ( a² + b² - c² ) .

⇒ ( a cos∅ - b sin∅ ) = √( a² + b² - c² ) .

Hence, \sf \pink { (a \: { \cos }^{2} \theta - b \: { \sin }^{2} \theta ) = \sqrt{ {a}^{2} + {b}^{2} - {c}^{2} } }.(acos

2

θ−bsin

2

θ)=

a

2

+b

2

−c

2

.