To find the exact value of csc10∘+csc50∘−csc70∘, we can follow these steps: Step 1: Rewrite the cosecant functions in terms of sineWe know that:cscθ=1sinθThus, we can rewrite the expression as:csc10∘+csc50∘−csc70∘=1sin10∘+1sin50∘−1sin70∘ Step ...
We start by rewriting the trigonometric functions in terms of sine and cosine:- cscθ=1sinθ- secθ=1cosθ- cotθ=cosθsinθ- tanθ=sinθcosθ Substituting these into the expression gives:(1sinθ−1cosθ)(cosθsinθ−sinθcosθ)(1sinθ+1cosθ)(1cosθ⋅1sinθ−2) Step 2...
照片 关于 三角轮廓矢量图图标 三角公式,如sin、cos、tan、cosec、sec和cot. 图片 包括有 功能, 抽象, 图标 - 184376356
If sin x + cos x = m(ne pm 1) and sec x + cosec x = n then n in terms of m is .
Step 1: Rewrite secant and cosecant in terms of sine and cosineRecall the definitions:- secθ=1cosθ so sec2θ=1cos2θ- cscθ=1sinθ so csc2θ=1sin2θ Substituting these into the expression gives: ⎛⎜⎝1cos2θ1sin2θ⎞⎟⎠+⎛⎜⎝1sin2θ1cos2θ⎞⎟⎠−(1...
Step 9: Rewrite secθ and tanθ in terms of sine and cosineLHS=2⋅1/cosθsinθ/cosθ=2⋅1sinθ=2cscθ Step 10: ConclusionThus, we have shown that:LHS=2cscθwhich is equal to the right-hand side (RHS). Final Resulttanθsecθ−1+tanθsecθ+1=2cscθ(Proved) ---Updated ...
2. Expressing in Terms of Sine and Cosine: We know: sec2α=1cos2αandcsc2α=1sin2α Therefore, we can rewrite the equation: 1=cos4θ⋅1cos2α+sin4θ⋅1sin2α This simplifies to: 1=cos4θcos2α+sin4θsin2α 3. Cross Multiplying: Multiply through by cos2αsin2α: cos4θ...
If sin^(-1)(1-x) sin^(-1)x=(pi)/(2) then x equal 04:07 If sin^(-1)(1-x)-2sin^(-1)x=cos^(-1)x, then x= 06:48 If tan^(-1)x+cos^(-1)((y)/(sqrt(1+y^(2)))=sin^(-1)((3)/(sqrt(10))), t... 07:35 Solve, (sec^- 1)x/a-(sec^- 1)x/b=sec...
If cos alpha + cos beta = 0 = sin alpha + sin beta, then value of cos... 04:07 If A + B = 45^(@), " then " (cot A - 1) ( cot B - 1) is 04:12 If alpha, beta in (0, (pi)/(2)), sin alpha = (4)/(5) " and " cos (alp... 06:00 The value of tan ...
Step 2: Express cscθ and sinθRecall that:cscθ=1sinθThus, we can rewrite the right-hand side:tanθ2=1sinθ−sinθ Step 3: Substitute sinθ in terms of tanθ2Using the half-angle identity for sine:sinθ=2tanθ21+tan2θ2Substituting this into the equation gives:tanθ2=12tanθ...