Tan 2theta formula

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Using the identity #tan2theta=(2tantheta)/(1-tan^2theta)# #tan4theta=(2tan2theta)/(1-tan^2(2theta)# = #(2xx(2tantheta)/(1-tan^2theta))/(1-((2tantheta)/(1-tan^2theta))^2# = #(2xx(2tantheta)/(1-tan^2theta))/(((1-tan^2theta)^2-4tan^2theta)/((1-tan^2theta))^2# = #(4tantheta)/(1-tan^2theta)xx(1-tan^2theta)^2/((1-tan^2theta)^2-4tan^2theta)# = #(4tantheta(1-tan^2theta))/((1+tan^4theta-2tan^2theta-4tan^2theta)# = #(4tantheta-4tan^3theta)/(1-6tan^2theta+tan^4theta)#

tan ⁡ ( θ ) = sin ⁡ ( θ ) cos ⁡ ( θ ) \tan(\theta)= \dfrac tan ( θ ) = cos ( θ ) sin ( θ ) ​ tangent, left parenthesis, theta, right parenthesis, equals, start fraction, sine, left parenthesis, theta, right parenthesis, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction cot ⁡ ( θ ) = cos ⁡ ( θ ) sin ⁡ ( θ ) \cot(\theta)= \dfrac cot ( θ ) = sin ( θ ) cos ( θ ) ​ cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, cosine, left parenthesis, theta, right parenthesis, divided by, sine, left parenthesis, theta, right parenthesis, end fraction sin ⁡ ( θ + ϕ ) = sin ⁡ θ cos ⁡ ϕ + cos ⁡ θ sin ⁡ ϕ sin ⁡ ( θ − ϕ ) = sin ⁡ θ cos ⁡ ϕ − cos ⁡ θ sin ⁡ ϕ cos ⁡ ( θ + ϕ ) = cos ⁡ θ cos ⁡ ϕ − sin ⁡ θ sin ⁡ ϕ cos ⁡ ( θ − ϕ ) = cos ⁡ θ cos ⁡ ϕ + sin ⁡ θ sin ⁡ ϕ \begin sin ( θ + ϕ ) sin ( θ − ϕ ) cos ( θ + ϕ ) cos ( θ − ϕ ) ​ = sin θ cos ϕ + cos θ sin ϕ = sin θ cos ϕ − cos θ sin ϕ = cos θ cos ϕ − sin θ sin ϕ = cos θ cos ϕ + sin θ sin ϕ ​ tan ⁡ ( θ + ϕ ) = tan ⁡ θ + tan ⁡ ϕ 1 − tan ⁡ θ tan ⁡ ϕ tan ⁡ ( θ − ϕ ) = tan ⁡ θ − tan ⁡ ϕ 1 + tan ⁡ θ tan ⁡ ϕ \begin tan ( θ + ϕ ) tan ( θ − ϕ ) ​ = 1 − tan θ tan ϕ tan θ + tan ϕ ​ = 1 + tan θ tan ϕ tan θ − tan ϕ ​ ​ Half angle identities sin ⁡ θ 2 = ± 1 − cos ⁡ θ 2 cos ⁡ θ 2 = ± 1 + cos ⁡ θ 2 tan ⁡ θ 2 = ± 1 − cos ⁡ θ 1 + cos ⁡ θ = 1 − cos ⁡ θ sin ⁡ θ = sin ⁡ θ 1 + cos ⁡ θ \begin sin 2 θ ​ cos 2 θ ​ tan 2 θ ​ ​ = ± 2 1 − cos θ ​ ​ = ± 2 1 + cos θ ​ ​ = ± 1 + cos θ 1 − cos θ ​ ​ = sin θ 1 − cos θ ​ = 1 + co...

• • • • Formula $\tan^2-1$ Therefore, it has derived that the square of tan function is equal to the subtraction one from the square of secant function.

• • • • Formula $\tan^2-1$ Therefore, it has derived that the square of tan function is equal to the subtraction one from the square of secant function.

Using the identity #tan2theta=(2tantheta)/(1-tan^2theta)# #tan4theta=(2tan2theta)/(1-tan^2(2theta)# = #(2xx(2tantheta)/(1-tan^2theta))/(1-((2tantheta)/(1-tan^2theta))^2# = #(2xx(2tantheta)/(1-tan^2theta))/(((1-tan^2theta)^2-4tan^2theta)/((1-tan^2theta))^2# = #(4tantheta)/(1-tan^2theta)xx(1-tan^2theta)^2/((1-tan^2theta)^2-4tan^2theta)# = #(4tantheta(1-tan^2theta))/((1+tan^4theta-2tan^2theta-4tan^2theta)# = #(4tantheta-4tan^3theta)/(1-6tan^2theta+tan^4theta)#

• Maths Menu Toggle • Basic Math • Binomial Theorem • Calculus Menu Toggle • Limits • Continuity • Complex Numbers • Geometry Menu Toggle • Circles • Triangles • Mathematical Induction • Matrices • Permutations And Combinations • Polynomials • Probability • Sequence and Series • Sets • Statistics • Vectors • Physics Menu Toggle • Current Electricity • Electrostatics • Engines • Fluid Mechanics • Gravitation • Heat • Light • Magnetic Effects of Electric Current • Magnetism And Matter • Mechanical Properties of Solids • Moving Charges and Magnetism • Optics • Radioactivity • Rotational Motion • Thermal Effects Of Electricity • Thermal Properties of Matter • Units and Measurement • X Rays • Chemistry Menu Toggle • Acids, Bases & Salts • Alcohols Phenols Ethers • Aldehydes Ketones Carboxylic Acids • Amines • Atom • Chemical Bonding • Chemical Constants • Chemical Equilibrium • Chemical Kinetics • Chromatography • Electrochemistry • Haloalkanes and Haloarenes • Periodic Table Menu Toggle • S-Block • P-Block • D-block • Reaction Mechanisms • States of Matter • Thermodynamics • Biology Menu Toggle • Biological Classification • Anatomy of Flowering Plants • Circulatory System • Ecology • Nutrition • Plant Growth and Development • Reproduction • Reproductive Health • Sexual Reproduction In Plants • Transportation In Plants • Skeletal System • Calculators • Job Listings • Index • • • • More About Tan Theta Tan theta formula can also be calculated from the ratio of the sine of the an...