CBSE Class 10 Maths: Trigonometry Question
(๐๐ − ๐๐)² − (๐๐ − ๐๐)² = (๐๐ − ๐๐)²
Answer:
a sec๐ + b tan๐ + c = 0
⇒ c = - (a sec๐ + b tan๐)
and p sec๐ + q tan๐ + r = 0
⇒ r = -(p sec๐ + q tan๐)
LHS = (๐๐ − ๐๐)² − (๐๐ − ๐๐)²
= [b(-p sec๐ - q tan๐) - q(-a sec๐ - b tan๐)]² - [p(-a sec๐ - b tan๐) - a(-p sec๐ - q tan๐)]²
= [-bp sec๐ - bq tan๐ + aq sec๐ + bq tan๐ ]² - [-ap sec๐ - bp tan๐ + ap sec๐ + aq tan๐]²
= [aq sec๐ - bp sec๐]² - [aq tan๐ - bp tan๐]²
= (aq - bp)²sec²๐ - (aq - bp)²tan²๐
= (aq - bp)²[sec²๐ - tan²๐]
= (aq - bp)² [∵ sec²๐ - tan²๐ = 1]
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