Question

3sina+5cosa=5
Then Prove That
5sina-3cosa=+/-(3)

Answer 1

3 sin a+ 5 cos a=5

Squaring
9 sin^2 a+30sin a+25 cos^2 a=25
9(1-cos^2 a) +30sinacos a +25(1-sin^2 a) =25
9-9cos^2a+30sin a cos a+25-25sin^2 a=25
-9cos^2a+30sin a cos a-25sin^2 a=-9
9=9cos^2 a-30sina cosa+25sin^2a
[+/-(3)] ^2 =(5 sin a-3 cos a) ^2
Cancelling square frm bith sides,
+/-(3)= (5 sin a-3 cos a)
Proved

Answer 2

Hey there !!

➡ Prove that :-

→ 5sin a - 3cos a = ±3.

▶ Solution :-

→ Given,

➡ 3sin a + 5cos a = 5.

Now,

→ ( 3sin a + 5cos a )² + ( 5sin a - 3sin a )² .

= 9sin²a + 25cos²a + 30sin a cos a + 25sin²a + 9cos²a - 30sin a cos a .

= 9( sin²a + cos²a ) + 25( sin²a + cos²a ) .

= 9 + 25.

= 34.


•°• ( 3sin a + 5cos a )² + ( 5sin a - 3cos a )² = 34.

=> 5² + ( 5sin a - 3cos a )² = 34. [ °•° 3sin a + 5cos a = 5 ]

=> 25 + ( 5sin a - 3cos a )² = 34.

=> ( 5sin a - 3cos a )² = 34 - 25.

=> ( 5sin a - 3cos a )² = 9.

[ Taking square root both side, we get ]

•°• ( 5sin a - 3cos a ) = ± 3.


✔✔ Hence, it is proved ✅✅.

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