The ages of rahul and sanjay are in the ratio 8: 9. ten years later, the sum of their ages is 105 years. what are their ages

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Here's your answer!!

Let their ages be equal to 8x and 9x.
After 10 years, their ages will be= 8x + 10 and 9x + 10

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8x/9x.
Ratio 8x:9x.
Ten years later,
8x+10+9x+10=105.
17x+20=105.
17x=85.
Therefore, x=85/17
x=5.
Therefore, 8x=40.
9x=45.
Their present ages are, 40 and 45.

Thank you.
Hope this will help you.

Say the coefficient is x.

8x : 9x
Ten years later the sum will be 105. Then:
8x+9x+10+10=105
(8x+9x)+20=105
17x+20=105

Use axioms to solve:
17x+20-20=105-20
17x=85
17x/17=85/17
x=5

Raul's age is now 8x = 40.
Sanjay's age is now 9x = 45.

Ans:  Raul is 40 and Sanjay is 45 yrs old.

Two com=plement angles different by 12=348

Take lhs:
(sina+cosa)/(sina-cosa)+(sina-cosa)/(sina+cosa)
=((sina+cosa)^2)+((sina-cosa)^2)/((sina-cosa)(sina+cosa))
=(sin^2a+cos^2a+2sinacosa+sin^2a+cos^2a-2sinacosa)/(sin^2a-cos^2a)
=2(sin^2a+cos^2a)/(sin^2a -cos^2a )
=2/(sin^2a -cos^2a )