Question

If a= p sec + q tan n b= p tan +q sec find a2 - b2

Answer 1

Answer:

Step-by-step explanation:

a=p sec + q tan

=p/cos + q sin/cos

=(p+qsin)/cos

b= p tan + q sec

=( psin + q)/cos

a^2-b^2=

( (p+qsin)^2 - (p sin +q) ) / Cos^2

=( p^2 + q^2sin^2 + 2 pqsin -p^2sin^2 -q^2 - 2pqsin ) / cos^2

=( p^2 - p^2sin^2 - q^2 + q^2sin^2 ) / cos^2

Take p^2 and q^2 common respectively

=( p^2(1-sin^2) - q^2 (1 - sin^2) ) / cos^2

Since,1-sin^2 = cos ^2

Therefore take common in numerator

= ( cos ^2 (p^2 - q^2) ) / cos ^2

= p^2 - q^2

Hope This will Help☺

Answer 2

Answer:

p²-q²

Step-by-step explanation:

a = p sec + q tan

a = p/cos  + q sin/cos

b = p tan  + q sec

b = p sin/cos  + q /cos

a² - b² = (a+b) (a-b)

= (p/cos  + q sin/cos +  p sin/cos  + q /cos)(p/cos  + q sin/cos - p sin/cos - q /cos)

= (1/cos) (p + qsin + psin + q) (1/cos)(p + qsin - psin - q)

= (1/cos)²(p(1+sin) + q (1+sin))((p(1-sin) - q(1-sin))

= (1/cos)²(p+q)(1+sin)(p-q)(1-Sin)

= (1/cos)²(p²-q²)(1 - sin²)

= (1/cos)²(p²-q²)(cos²)

= p²-q²