Question
Download Solution PDFযদি sin x + cos x = √2 sin x হয়, তাহলে sin x - cos x এর মান কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
sin x + cos x = √2 sin x
ব্যবহৃত সূত্র:
ত্রিকোণমিতিক অভেদ এবং বীজগণিতীয় কৌশল
a2 - b2 = (a - b) x (a + b)
গণনা:
প্রদত্ত সমীকরণ দিয়ে শুরু করুন:
sin x + cos x = √2 sin x
উভয় পক্ষে বর্গ করুন
(sin x + cos x)2 = (√ 2sinx)2
⇒ sin2x + cos2x + 2sinxcosx = 2sin2x
⇒ 2sinxcosx = sin2x - cos2x
⇒ 2sinxcosx = (sinx - cosx) x (sin x + cos x)
⇒ 2sinxcosx = (sinx - cosx) x √ 2sinx
⇒ √ 2cosx = (sinx - cosx)
সঠিক উত্তরটি হলো বিকল্প 4.
Last updated on Jun 17, 2025
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