Explanation
Simplifying the above equation we get
cosA1−tanA+sinA1−cotA
=cosA1−sinAcosA+sinA1−cosAsinA
=cos2AcosA−sinA+sin2AsinA−cosA
=cos2A−sin2AcosA−sinA
=(cosA−sinA)(cosA+sinA)cosA−sinA
=cosA+sinA
Hence answer is B
Expanding the given expression we get
(cosA+sinA)2−(cosA+sinA)2
=cosA2+sinA2+2cosAsinA−(cosA2+sinA2−2cosAsinA)
=2(2cosAsinA)
=4cosAsinA
Hence, option D is correct.
By expanding the expression we get
(sinθ+cscθ)2+(cosθ+secθ)2−(tan2θ+cot2θ)
=sin2θ+csc2θ+2+sec2θ+cos2θ+2−tan2θ−cot2θ
=4+(sin2θ+cos2θ)+(csc2θ−cot2θ)+(sec2θ−tan2θ)
=4+1+1+1=7
Hence answer is D
Simplifying the given expression we get
sinαcosαsin2αtanα+sinαcosα
=sinα(sinαcosα)(sinαtanα+cosα) ...(taking sinα common from the denominator)
=1sinαtanαcosα+cos2α
=1sin2α+cos2α
=1
cosA=2sinA
Dividing by sinAon both the sides we get
cotA=2 ...(i)
cosec2A=1+cot2A
cosec2A=1+22 ...(from i )
cosec2A=5
Therefore
cosecA=±√5
(sin2θ+cos2θ)3=1
sin6θ+cos6θ+3sin2θcos2θ(sin2θ+cos2θ)=1
sin6θ+cos6θ+3sin2θcos2θ(1)=1
Hence answer is C
4cos2θ−2√2cosθ−1=0 cosθ=2√2±√8+168=√2±√64 cosθ=√6+√24 ⇒θ=π12;2π−π12=23π12 cosθ=−√6−√24 cosθ=cos(π−5π12);cos(π+5π12) θ=7π12;17π12 Hence option B is the correct option
α+β=900 ...(i)
α−2β=0 ...(ii)
Subtracting ii from i we get
3β=900
β=300
cos2α+sin2β
=cos2(900−β)+sin2β ...from(i)
=sin2β+sin2β
=2sin2β
Substituting the value of β we get
2sin2β=2(12)2
=12
Hence the answer is A
n|sin(x)|=m|cos(x)| nm=|cot(x)| Or mn=|tan(x)| Or tan(x)=mn Hence x=tan−1(mn) and x=π+tan−1(mn). And tan(x)=−mn Hence x=−tan−1(mn) and x=π−tan−1(mn). Now if n,m≠0 we therefore get 4 solutions in the interval of [0,2π] independent of the values of m and n.
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