Questions
detailed solution
Correct option is C
We have __A=cosθ−sinθsinθcosθ∴ |A|=cos2θ+sin2θ=1 And adj A=cosθsinθ−sinθcosθ∵ If A=a bc d, then adj A=d−b−ca⇒ A−1=cosθsinθ−sinθcosθ ∵A−1=adj A|A| Note that, A−50=A−150 Now, A−2=A−1A−1⇒A−2=cosθsinθ−sinθcosθcosθsinθ−sinθcosθ=cos2θ−sin2θcosθsinθ+sinθcosθ−cosθsinθ−cosθsinθ−sin2θ+cos2θ=cos2θsin2θ−sin2θcos2θ Also, A−3=A−2A−1A−3=cos2θsin2θ−sin2θcos2θcosθsinθ−sinθcosθ=cos3θsin3θ−sin3θcos3θ Similarly, A−50=cos50θsin50θ−sin50θcos50θ=cos256πsin256π−sin256πcos256π when θ=π12=cosπ6sinπ6−sinπ6cosπ6∵cos25π6=cos4π+π6=cosπ6 and sin25π6=sin4π+π6=sinπ6=3212−1232Similar Questions
If , then is
799 666 8865
support@infinitylearn.com
6th Floor, NCC Building, Durgamma Cheruvu Road, Vittal Rao Nagar, HITEC City, Hyderabad, Telangana 500081.
JEE Mock Tests
JEE study guide
JEE Revision Notes
JEE Important Questions
JEE Sample Papers
JEE Previous Year's Papers
NEET previous year’s papers
NEET important questions
NEET sample papers
NEET revision notes
NEET study guide
NEET mock tests