Question
Download Solution PDFयदि ABCD एक चक्रीय चतुर्भुज है, तो cos2A – cos2B – cos2C + cos2D का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
चक्रीय चतुर्भुज के सम्मुख कोण संपूरक होते हैं।
इसलिए,
A + C = 180°, ⇒ C = 180° - A
B + D = 180°, ⇒ D = 180 - B
अब,
cos2A – cos2B – cos2C + cos2D
⇒ cos2A – cos2B – cos2(180 - A) + cos2(180 - B)
⇒ cos2A – cos2B – {cos(180 - A)}2 + {cos(180 - B)}2
⇒ cos2A – cos2B – {- cos A}2 + {- cos B}2
⇒ cos2A – cos2B – cos2A + cos2B
⇒ cos2A – cos2A – cos2B + cos2B
⇒ 0 - 0 = 0
अतः, सही उत्तर विकल्प (3) है।
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