Question

if cos. alfa / cos. beta= m, cos. alfa/ sin. beta= n, then prove that ( m^2+ n^2) cos. beta= n^2​

Answer 1

proved in the explanation

Step-by-step explanation:

take

alfa = a and beta = b ..... for better understanding

→ cos a = m ......→ 1

cos b

→ cos a = n .......→2

sin b

by cross multiply of 1 and 2

we get

→ cos a = ( cos b)m

→ cos b = ( sin b)n

equating both we get

→(cos b)m = n(sin b)

squaring on both sides we get

→ cos ²b(m²) = (sin ²b) n²

→ (cos ²b)m²= (1 - cos ²b)n²

→ (cos ²b)m² = n² - (n²) cos ²b

→ (m² + n²) cos ²b = n²

i hope u understood this solution